<Text-field style="Heading 1" layout="Heading 1">Introduction</Text-field>

<Text-field style="Heading 1" layout="Heading 1">Fourier Series</Text-field>

<Text-field style="Heading 2" layout="Heading 2">The <Font family="Arial">FourierSeries</Font> Command</Text-field>

JSFH

The simplest calling sequence for applying the FourierSeries command to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInhGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ== is

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEuRm91cmllclNlcmllc0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYtLUYsNiVRImZGJ0YvRjItRjY2JC1GIzYkLUYsNiVRInhGJ0YvRjIvRjNRJ25vcm1hbEYnRkQtSSNtb0dGJDYtUSIsRidGRC8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0ZMLyUqc3ltbWV0cmljR0ZMLyUobGFyZ2VvcEdGTC8lLm1vdmFibGVsaW1pdHNHRkwvJSdhY2NlbnRHRkwvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4zMzMzMzMzZW1GJ0ZBLUZHNi1RIj1GJ0ZERkovRk5GTEZPRlFGU0ZVRlcvRlpRLDAuMjc3Nzc3OGVtRicvRmduRl5vLUYsNiVRImFGJ0YvRjItRkc2LVEjLi5GJ0ZERkpGXG9GT0ZRRlNGVUZXL0ZaUSwwLjIyMjIyMjJlbUYnL0ZnbkZlbi1GLDYlUSJiRidGL0YyRkYtRiw2JVEibkYnRi9GMkZERkRGRA==

JSFH

where LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, the number of terms, can be "infinity". This command would return a Fourier sine-cosine series. If LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= is a finite number, then a partial sum of the series would be returned; otherwise a formal sum to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= is returned.

A more general form of this command would be

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

JSFH

where 'CoefficientName' is the name of a variable to which will be assigned the coefficients of the returned series, and options are equations detailed in Table 3.

Option Name

Option Value

Option Effect

output =

inert

symbolic

numericJSFH

Returns a formal sum

Default

Coefficients obtained via numeric integration

series =

trigonometric

exponential

polar

hartley

cosine

sine

Default (sine-cosine series)

(See below)

Cosine series

Sine series

constant =

true

false

Default (Maple computes LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMEYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdGPUY+, the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjBGJ0Y5Rjk= coefficient)

Coefficient LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMEYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdGPUY+ is assumed to be zero

intoptions =

[...]

Default is ['AllSolutions']

evalfIntoptions =

[...]

Default is [digits=6, maxintervals = 10 000]

Table 3 Options available for the FourierSeries command applied to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInhGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ==

JSFH

The default (trigonometric) form of the Fourier series for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInhGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ== is 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, where 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. Since

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYwLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIn5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSRjb3NGJy9GMEY9RjktSShtZmVuY2VkR0YkNiQtRiM2Ji1GLDYlUScmIzk2OTtGJ0ZSRjlGNS1GLDYlUSJ4RidGL0YyRjlGOS1GNjYtUSIrRidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnL0ZORlxvLUYsNiVRImJGJ0YvRjJGNS1GLDYlUSRzaW5GJ0ZSRjlGUy1GNjYtUSI9RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjI3Nzc3NzhlbUYnL0ZORmhvLUkmbXNxcnRHRiQ2Iy1GIzYmLUklbXN1cEdGJDYlRistRiM2JS1JI21uR0YkNiRRIjJGJ0Y5Ri9GMi8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGaG4tRmBwNiVGXm9GYnBGaHBGOUZPLUZUNiQtRiM2KUZYRjVGZW4tRjY2LVEoJm1pbnVzO0YnRjlGO0Y+RkBGQkZERkZGSEZbb0Zdby1GLDYlUSdhcmN0YW5GJ0ZSRjktRlQ2JC1GIzYmRl5vLUY2Ni1RIixGJ0Y5RjsvRj9GMUZARkJGREZGRkhGSi9GTlEsMC4zMzMzMzMzZW1GJ0YrRjlGOUY5RjlGOQ==

the trig form of the Fourier series is equivalent to the polar form

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

The basis functions in the exponential option are 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, whereas for the hartley option they are

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 and 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

<Text-field style="Heading 2" layout="Heading 2">Example 1</Text-field>

JSFH

Apply the FourierSeries command to 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.

JSFH

First, let the number of terms be the indeterminate LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=. The default index in the OrthogonalExpansions package is LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiaUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=.

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LCYjIiIiIiIjRiQtSSRTdW1HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JCwkKihJI1BpR0YpISIiSSJpR0YrRjAtSSRzaW5HRig2IywkKipGJUYkRi9GJEYxRiRJInhHRitGJEYkRiRGMC9GMTtGJEkibkdGK0Yk

JSFH

To change the index, use the subs command.

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LCYjIiIiIiIjRiQtSSRTdW1HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JCwkKihJI1BpR0YpISIiSSJrR0YrRjAtSSRzaW5HRig2IywkKipGJUYkRi9GJEYxRiRJInhHRitGJEYkRiRGMC9GMTtGJEkibkdGK0Yk

JSFH

For some expansions, it is possible to get a "closed form" for the partial sum.

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LCYjIiIiIiIjRiQqKiomRiNGJF4jRiRGJEYkSSNQaUclKnByb3RlY3RlZEchIiJJIm5HNiJGKywuKiYtSSNsbkc2JEYqSShfc3lzbGliR0YtNiMsJkYkRiQtSSRleHBHRjI2IyooKiZGJUYkRihGJEYkRilGJEkieEdGLUYkRitGJEYsRiRGKyooLUY3NiMqKkY6RiRGKUYkRjtGJEYsRiRGJC1JKUxlcmNoUGhpR0YzNiVGNkYkRixGJEYsRiRGK0Y9RiQqKC1GNzYjLCQqKiwkRjpGJEYkRilGJEY7RiRGLEYkRitGJC1GQTYlLUY3NiMsJCooRkhGJEYpRiRGO0YkRitGJEYsRiRGLEYkRiQqJi1GMTYjLCZGJEYkRktGK0YkRixGJEYkRkRGK0YkRiQ=

The full formal expansion:

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LCYjIiIiIiIjRiQtSSRTdW1HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JCwkKihJI1BpR0YpISIiSSJpR0YrRjAtSSRzaW5HRig2IywkKipGJUYkRi9GJEYxRiRJInhHRitGJEYkRiRGMC9GMTtGJEkpaW5maW5pdHlHRilGJA==

For some formal expansions, a closed-form of the sum can be obtained.

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LCYjIiIiIiIjRiQqJiwmKiZGI0YkLUknYXJjdGFuRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQsJC1JJHNpbkdGKzYjLCQqKEYlRiRJI1BpR0YsRiRJInhHRi5GJEYkISIiLCZGJEYkLUkkY29zR0YrRjNGOEYkRiQqJkYjRiQtRio2JEYxRjlGJEY4RiRGNkY4RiQ=

Since the full formal sum does not reduce to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=, obtain its graph.

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

-%%PLOTG6)-%'CURVESG6)7dw7$$!+%*******H!"*$"2N>()[BbWi&!#D7$$!2a'z.*QUZ*H!#;$"1'3N?'4hd_!#=7$$!22ws]xn,*H!#;$"13&Rs#\AK)*!#=7$$!2$[\AVJ-&)H!#;$"2G<0vn&o(\"!#=7$$!2ju<%4W%)zH!#;$"13aAe!fb,#!#<7$$!2$R$G#*G!puH!#;$"1$3mr2r4`#!#<7$$!22XR+w6*pH!#;$"2M%\0'*R#)3I!#=7$$!1pv%)pQ'\'H!#:$"1,JC:Ih.N!#<7$$!2`4LZvY)fH!#;$"110pEXK:S!#<7$$!20pr-0YZ&H!#;$"2&f4$G(\RDX!#=7$$!1iox[$*\\H!#:$"2;!QJA^1]]!#=7$$!2xPW70y[%H!#;$"1EAcv[>7b!#<7$$!1WTxkbnRH!#:$"1,ceANWKg!#<7$$!2$>YR;<XMH!#;$"04Q0OG[b'!#;7$$!1"QD0d<%HH!#:$"1o=YZHCeq!#<7$$!2$>jz$3Y[#H!#;$"1%3o.i"R:v!#<7$$!2;!="R95%>H!#;$"1Y)>)3c)*e!)!#<7$$!12iz*=0["H!#:$"1x#z.-"[>&)!#<7$$!1E$GM`[%4H!#:$"1'RnrlY^0*!#<7$$!2)fA*[)pq/H!#;$"0.u2^,$H&*!#;7$$!1zJlaZ]**G!#:$"2U@oMX_\+"!#<7$$!2tGX7+^X*G!#;$"1Fra()**[a5!#;7$$!22,Z#zAQ*)G!#;$"2J*)Hv?xh5"!#<7$$!2(4A&*ydj%)G!#;$"2V!zZ5Ak`6!#<7$$!0Nar.;&zG!#9$"/lXG'R[?"!#97$$!1$f.V1)>uG!#:$"2'pS'pN>!e7!#<7$$!2$oQI`(o&pG!#;$"2aJhpY7VI"!#<7$$!1Z+gq*oX'G!#:$"1N&**RH5VN"!#;7$$!2%4z$eq.%fG!#;$"2_!4iTH'fS"!#<7$$!2(\*y>]]V&G!#;$"2:]5-)\\c9!#<7$$!10XTn7Y\G!#:$"2F&\&eK(Q0:!#<7$$!2COAggKS%G!#;$"2aPw(RRnf:!#<7$$!1`?J7Z:RG!#:$"2"o%zo(GX3;!#<7$$!2Bt5'>l%R$G!#;$"2#yE*Q![`g;!#<7$$!2lpLH7F#HG!#;$"2c.j1xGxq"!#<7$$!2;o4ednS#G!#;$"2d=.>CC$f<!#<7$$!1$*)eS%G@>G!#:$"2<26%f:(y!=!#<7$$!2)[>b]#QT"G!#;$"2X^![%\<'e=!#<7$$!1mw%y!p<4G!#:$"2BMB:#4B3>!#<7$$!2FfH=%G)R!G!#;$"1sSq"er,'>!#;7$$!2()zC*Q.)*)z#!#;$"2`,_2h'>5?!#<7$$!2G9xrbkQz#!#;$"2GdG#GWNh?!#<7$$!2-E&oO6z)y#!#;$"2/SZJj)37@!#<7$$!2()Ge,>HTy#!#;$"1;rT)43(e@!#;7$$!1%)zLtgyyF!#:$"21;?mER@@#!#<7$$!2a9ef72Sx#!#;$"1Z&=/uG*fA!#;7$$!1scHr<"*oF!#:$"1#GVqG#)3J#!#;7$$!1z5tm[.kF!#:$"2F@*oK8lfB!#<7$$!1:p'4p>'eF!#:$"2)[3L!4.QT#!#<7$$!1E8lY0$Rv#!#:$"1Vn[LXpgC!#;7$$!1s6"fK3'[F!#:$"2&z#))3u;R^#!#<7$$!1op[*pdPu#!#:$"1A.80IUiD!#;7$$!16`[w=XQF!#:$"1$*o9N7[:E!#;7$$!2wH]&[Q(Qt#!#;$"2k-(\9:EhE!#<7$$!1w`64+mGF!#:$"1Ti%)3**R8F!#;7$$!2L-=wpBOs#!#;$"1p(>Q-jPw#!#;7$$!1L6Aw1f=F!#:$"1r')yPK49G!#;7$$!0">Sqhd8F!#9$"2$**3)fHQU'G!#<7$$!16#e,!)e(3F!#:$"1#*yT)*>T7H!#;7$$!28LY`4^Nq#!#;$"0pOl/*[kH!#:7$$!2F8a]x(e)p#!#;$"1w'e%\A79I!#;7$$!1V?;9TO$p#!#:$"1t&z$e)ej1$!#;7$$!2/^jJWN')o#!#;$"1)*[Oobk8J!#;7$$!2Yb#\w$4Mo#!#;$"1aW2Ni!f;$!#;7$$!1TjH:PSyE!#:$"1(eOq%G'f@$!#;7$$!2(z&>!Q-TtE!#;$"2X?/)>w*eE$!#<7$$!2t+];`%>oE!#;$"1G**\$oa!=L!#;7$$!1.vnv1RjE!#:$"1p\AVK4mL!#;7$$!2&["e+(3ZeE!#;$"1:&=%*H"H:M!#;7$$!1#3t+#)QIl#!#:$"1#=p#*z6'pM!#;7$$!2;>]Pa?"[E!#;$"2w3)\iXz=N!#<7$$!1Hj'\o!4VE!#:$"2CrO.:$4pN!#<7$$!2&*GV"[a(zj#!#;$"2t5n&=bC?O!#<7$$!0E4,btKj#!#9$"2FS2*)\ksm$!#<7$$!1xQ1z9EGE!#:$"1J7O4_Q<P!#;7$$!1#4H-c(GBE!#:$"2'z!4xRCrw$!#<7$$!0EdJ,nzh#!#9$"1,uUo)H.#Q!#;7$$!1$z^3'=F8E!#:$"2'o?["R"GnQ!#<7$$!1@5wHY&yg#!#:$"1#z*Q-PX@R!#;7$$!2vM_j*f'Hg#!#;$"1DlZO+MqR!#;7$$!0'R7\*G")f#!#9$"1,/w30r=S!#;7$$!1LwVpv#Hf#!#:$"1rOi0VsqS!#;7$$!1#H)4\^q(e#!#:$"293<!4&[H7%!#<7$$!1H)e)>N&He#!#:$"12<T,[YqT!#;7$$!0:t1]2zd#!#9$"2&*\oK*\#4A%!#<7$$!1.U7zI)Hd#!#:$"0(zv3#p,F%!#:7$$!1'Q8U&\knD!#:$"1Rh'yX]NK%!#;7$$!12v+#*f-jD!#:$"1K\#*z+upV!#;7$$!2bw!*f%4sdD!#;$"1YB4S0zAW!#;7$$!2YbRQ#Rt_D!#;$"1dWgh2msW!#;7$$!2`u$)32&zZD!#;$"2aai6H\?_%!#<7$$!27^L!*G_Ga#!#;$"2w)[m4rZrX!#<7$$!0k?W'4"y`#!#9$"2.g$zb.*=i%!#<7$$!2EF'yWsYKD!#;$"1vs8_vKvY!#;7$$!2kicrdnv_#!#;$"1OPVGUKCZ!#;7$$!2n))eg(4tAD!#;$"2E86%R-psZ!#<7$$!2Ov&3H2c<D!#;$"1lC94FRC[!#;7$$!1l$)GP<S7D!#:$"2([j6FE)f([!#<7$$!1UhyN7x2D!#:$"2'y&Q@k(GA\!#<7$$!2)))o$G2'G-D!#;$"2D6J;FRr(\!#<7$$!2XrTGM'p(\#!#;$"1cGerl.B]!#;7$$!17?3Q"GB\#!#:$"1z)z">'=n2&!#;7$$!2m?'o1Z?([#!#;$"1Nz8LH&z7&!#;7$$!1-5s#4IE[#!#:$"1#)**ys!*pt^!#;7$$!2&*=t3Y&[xC!#;$"11"o7RX^A&!#;7$$!2v)f1FnIsC!#;$"1D,MHF$pF&!#;7$$!21ewog_rY#!#;$"1(>M7$RZG`!#;7$$!1#p(oxSPiC!#:$"1$3BJAfiP&!#;7$$!2."e\(=EuX#!#;$"1**=/D"QdU&!#;7$$!1O8Qs!4BX#!#:$"0k'=w#4pZ&!#:7$$!2<$*>zO3sW#!#;$"1$o+3K;z_&!#;7$$!1.^Um;'>W#!#:$"1r*[dL$Q!e&!#;7$$!1>E*)o.MPC!#:$"0"Q26jfEc!#:7$$!1'QAC)y8KC!#:$"1Whxv6iyc!#;7$$!20'G/MS"pU#!#;$"1(Rr&f'f3t&!#;7$$!2Bit")))z=U#!#;$"1xPE=6?"y&!#;7$$!20cW9S3tT#!#;$"1&Rab)f"p#e!#;7$$!1V+chC(=T#!#:$"1s&*R%Qv7)e!#;7$$!2$[WW2vE2C!#;$"1=bbD\KFf!#;7$$!2ucw5&3">S#!#;$"1EVB*["*3)f!#;7$$!1,0a-$prR#!#:$"0*\fupIGg!#:7$$!0U,B2n>R#!#9$"1*z&)pFH.3'!#;7$$!2&GN*)=L,(Q#!#;$"1:Z16o')Hh!#;7$$!2:D&*ofW=Q#!#;$"1'[Z5.a:='!#;7$$!1^/g'4)4xB!#:$"1"\&*R.>!Hi!#;7$$!27f-[Ny>P#!#;$"1*3u>X;-G'!#;7$$!1M=&>QgmO#!#:$"0m"[!='RLj!#:7$$!2&4@&42J?O#!#;$"10*y/H*ozj!#;7$$!1)G[#)GJqN#!#:$"1Ar^<roHk!#;7$$!21:'[Bg'=N#!#;$"1&\Q^wR8['!#;7$$!1">F'>G"oM#!#:$"1"4GP!=(=`'!#;7$$!2iui]eB>M#!#;$"0as$\Tw!e'!#:7$$!2OgqO#\\OB!#;$"1mRHj20Nm!#;7$$!2VHg*HqhJB!#;$"1eqR+(HQo'!#;7$$!2N(*es$)3kK#!#;$"1l-TF;"ft'!#;7$$!2x$>eS%*o@B!#;$"1B1=%f0Jy'!#;7$$!1BzX$*)HlJ#!#:$"1s2Ul5qMo!#;7$$!1Mrqh^n6B!#:$"1i'GHQ[K)o!#;7$$!0>+#o0g1B!#9$"1-")*zJ%*R$p!#;7$$!12f\D#R;I#!#:$"0$4/Xxg$)p!#:7$$!1MyZf^W'H#!#:$"1i;A0%[b.(!#;7$$!0/tllU9H#!#9$"1-'pUVtb3(!#;7$$!1%QD[(oK'G#!#:$"1ihu^7tOr!#;7$$!1,NLaMD"G#!#:$"1"*\mcaY(=(!#;7$$!0`1y]"fwA!#9$"/Z$>#\3Ms!#97$$!2cA')4R[7F#!#;$"1Wx8!4;vG(!#;7$$!2mQ1OWpkE#!#;$"1Mh$Rc0`L(!#;7$$!18R%*)3u8E#!#:$"1p3c5"fiQ(!#;7$$!2-KzV=(\cA!#;$"/o?c"G]V(!#97$$!1d^h3?3^A!#:$"1M%[Q"*z"*[(!#;7$$!1n&*HkGRYA!#:$"0L/qNrg`(!#:7$$!2MTfNkq5C#!#;$"1neSkNH*e(!#;7$$!14_8<+AOA!#:$"14zkG)*zPw!#;7$$!1_N8%>94B#!#:$"1yWme!e3p(!#;7$$!1R&)>mhLEA!#:$"19Y,Q$Qmt(!#;7$$!2thjnKA6A#!#;$"1HQOKnx)y(!#;7$$!2XEm_,'3;A!#;$"1ctLZ)R"Ry!#;7$$!1u$pQ*H06A!#:$"1hiIh+Z*)y!#;7$$!28:]!)[Qg?#!#;$"1([)\>^hRz!#;7$$!1_k!y6@7?#!#:$"0[N>#))y()z!#:7$$!2Dd%*HT8g>#!#;$"1vU0qe')R!)!#;7$$!2NP-F4]5>#!#;$"1li(H2*\*3)!#;7$$!1%G5=VEe=#!#:$"0;(*=oN<9)!#:7$$!2<v63w(4"=#!#;$"1%[#)=RA!*=)!#;7$$!1'zSTpre<#!#:$"1W?feIGT#)!#;7$$!2CeWH.m3<#!#;$"1yTbq'R8H)!#;7$$!1@ymbD(e;#!#:$"1"z@LWu7M)!#;7$$!2&[#)H\olg@!#;$"1:v,2:V$R)!#;7$$!2QuDL*H&e:#!#;$"1iDum+ZT%)!#;7$$!2(*Q1x=L4:#!#;$"1.h$H7o1\)!#;7$$!1B8sP6]X@!#:$"1pnyA'))\a)!#;7$$!1L%)RhGeS@!#:$"1uc,'QrTf)!#;7$$!0d9E+`b8#!#9$"1)HaQ(*pWk)!#;7$$!23`"zlxVI@!#;$"1&p%3UBi&p)!#;7$$!1,vvnetD@!#:$"1*)\UA8kU()!#;7$$!2%=@r'zB27#!#;$"1=)yG.iFz)!#;7$$!1Lt(y()\d6#!#:$"0nE7A,D%))!#:7$$!1,b!3LH/6#!#:$"1*)\%>p1d*))!#;7$$!2V.+&yTt0@!#;$"1f'**\@eE%*)!#;7$$!1i#4u%pJ+@!#:$"1#Q2f_Io**)!#;7$$!1*e+SJGa4#!#:$"13T**forX!*!#;7$$!2:?snE"f!4#!#;$"1&)zFKt3%4*!#;7$$!2U(e3())*Q&3#!#;$"1e79H65Y"*!#;7$$!2L`YnYn,3#!#;$"1oY`K`K)>*!#;7$$!2/22v$eTv?!#;$"1'HH\iTeC*!#;7$$!29R@$=)p.2#!#;$"1'3'y;=I'H*!#;7$$!1WCx'RXa1#!#:$"1ebFKgaX$*!#;7$$!2tih=F2,1#!#;$"1HPQ"GF*)R*!#;7$$!2'[dl4$)[b?!#;$"1;DW.p6X%*!#;7$$!12!ROE$=]?!#:$"1J*4OOn")\*!#;7$$!2ez([Ti>X?!#;$"1W?7&eP![&*!#;7$$!2m)>`)Qd-/#!#;$"1N,o9hU(f*!#;7$$!2Dv"o1YJN?!#;$"1vC=LR&ok*!#;7$$!29))o?Gt-.#!#;$"1*=6$zrE(p*!#;7$$!2M^MCcH\-#!#;$"1o[lvVq](*!#;7$$!2w'[![*)H+-#!#;$"1F8&>0,(*z*!#;7$$!1Grq$H$>:?!#:$"1B(GH1n![)*!#;7$$!1&*RtYI-5?!#:$"1b+mK&p(**)*!#;7$$!2kgO\0k[+#!#;$"1KRj]%f8&**!#;7$$!+1+++?!"*$"1WavV********!#;7dw7$$!+'*******>!"*$"2&>)4%)RT$=U!#D7$$!1Np,"RUZ*>!#:$"1V]1$)*3wD&!#=7$$!2;VLqxn,*>!#;$"0mol'HAK)*!#<7$$!24/l^9B])>!#;$"2_#f\$[&o(\"!#=7$$!1CrL6W%)z>!#:$"1)f(Gm)eb,#!#<7$$!225F6H!pu>!#;$"2<&**G()3(4`#!#=7$$!2y4>>w6*p>!#;$"1L-43Q#)3I!#<7$$!2XU2<(Q'\'>!#;$"2'ovDHGh.N!#=7$$!2A[slvY)f>!#;$"1v<vUVK:S!#<7$$!2[n!4_gua>!#;$"1TD$4z%RDX!#<7$$!2#f[d]$*\\>!#;$"2k29D%\1]]!#=7$$!0*Q-`!y[%>!#9$"1*)4h(p%>7b!#<7$$!2n%G`mbnR>!#;$"1L`rYLWKg!#<7$$!2jUK"=<XM>!#;$"1btv'=G[b'!#<7$$!280VAd<%H>!#;$"1n[pvFCeq!#<7$$!2Nq&\&3Y[#>!#;$"1a'H/X"R:v!#<7$$!2BW*eX,T>>!#;$"1md0Ta)*e!)!#<7$$!2wUb9>0[">!#;$"1csXa3[>&)!#<7$$!2,7m]`[%4>!#;$"1$)zQ$\Y^0*!#<7$$!2x36l)pq/>!#;$"1G7*)[8IH&*!#<7$$!1)>^iv/&**=!#:$"1A!)[PC&\+"!#;7$$!28\BG+^X*=!#;$"2u3l<(**[a5!#<7$$!2(RX!3G#Q*)=!#;$"2Ega>>xh5"!#<7$$!2Gv!\!yNY)=!#;$"2>Z#4&>UO:"!#<7$$!2VTs'Qg^z=!#;$"2)eeF8'R[?"!#<7$$!2_Q+e1)>u=!#;$"2x9'*>M>!e7!#<7$$!2L9#ya(o&p=!#;$"2lcy@X7VI"!#<7$$!2DKe?(*oX'=!#;$"2mx;%z-Ja8!#<7$$!1CbF2PSf=!#:$"1hZCFH'fS"!#;7$$!2<N'R.0Na=!#;$"1&[Og'\\c9!#;7$$!0N7)o7Y\=!#9$"2F]w=J(Q0:!#<7$$!2F\)R2E.W=!#;$"2L2:g#Rnf:!#<7$$!1s'oOra"R=!#:$"2FG8L'GX3;!#<7$$!2#=l%4_YR$=!#;$"2y"[`!zM0m"!#<7$$!101DCrAH=!#:$"2/&R\d(Gxq"!#<7$$!2=&f5xv1C=!#;$"1#[S*GUKf<!#;7$$!2VuN`%G@>=!#;$"2xbUmary!=!#<7$$!2>]3=DQT"=!#;$"1#)\">[<'e=!#;7$$!2PP%34p<4=!#;$"2bEc"44B3>!#<7$$!1Cb/VG)R!=!#:$"2-wW&p:<g>!#<7$$!0s?,M!)*)z"!#9$"1*z#z)f'>5?!#;7$$!27g_$eX'Qz"!#;$"2$))RZ;WNh?!#<7$$!2YUSy8"z)y"!#;$"1`df@')37@!#;7$$!2c![H">HTy"!#;$"2[%>0(33(e@!#<7$$!2$GJXugyy<!#;$"1<(oaDR@@#!#;7$$!1uT0Fr+u<!#:$"1i#e%H(G*fA!#;7$$!2)=8Ps<"*o<!#;$"2D"oGwA)3J#!#<7$$!2%=syn[.k<!#;$"2l"y7A8lfB!#<7$$!2TR,?p>'e<!#;$"2)eg)*zI!QT#!#<7$$!2"[qmZ0$Rv"!#;$"1=&HL_%pgC!#;7$$!2cg0pK3'[<!#;$"1VR%4t;R^#!#;7$$!2')*>Y+xvV<!#;$"2E,!Q&*HUiD!#<7$$!2(="Ru(=XQ<!#;$"2M")3cA"[:E!#<7$$!1$z&[\Q(Qt"!#:$"222U^]h7m#!#<7$$!2l,I+,g'G<!#;$"2l$)*p**)*R8F!#<7$$!1=D^)pBOs"!#:$"1A[([,jPw#!#;7$$!2b\&4x1f=<!#;$"1Y]/HK49G!#;7$$!2[@c7<wNr"!#;$"2D&yV(GQU'G!#<7$$!2iC$*4!)e(3<!#;$"2%Rv1!*>T7H!#<7$$!1O0;'4^Nq"!#:$"2$RYRQ!*[kH!#<7$$!2P[[ex(e)p"!#;$"2D;::CAT,$!#<7$$!2#*\N\6kLp"!#;$"0,X1&)ej1$!#:7$$!2A0=RWN')o"!#;$"1z%>3cXO6$!#;7$$!2A>EsP4Mo"!#;$"1z!QxA1f;$!#;7$$!1c*4gr.%y;!#:$"1R/!*RG'f@$!#;7$$!21A8(Q-Tt;!#;$"1'znGh(*eE$!#;7$$!2ayAB`%>o;!#;$"1Z@xwY0=L!#;7$$!2b1Jjn!Rj;!#;$"1X$*oOK4mL!#;7$$!2@.#pq3Ze;!#;$"1y'zIH"H:M!#;7$$!1P_o?)QIl"!#:$"1Hw9$z6'pM!#;7$$!2RnUVa?"[;!#;$"1iKdcXz=N!#;7$$!2:pQbo!4V;!#;$"2Z38Y9$4pN!#<7$$!29>&p[a(zj"!#;$"1(3[I^X-i$!#;7$$!2WNU1btKj"!#;$"1ckd$\ksm$!#;7$$!2K#pdz9EG;!#;$"1n2B/_Q<P!#;7$$!2BCA2c(GB;!#;$"2mdxFRCrw$!#<7$$!2#G"HO,nzh"!#;$"1>(3P')H.#Q!#;7$$!2/)[Ih=F8;!#;$"1(>^pQ"GnQ!#;7$$!2#RC>IY&yg"!#;$"13c2)p`9#R!#;7$$!2=@kn*f'Hg"!#;$"29)yNK+MqR!#<7$$!2fZ;&\*G")f"!#;$"1V_$[]5(=S!#;7$$!2KM4)pv#Hf"!#;$"2'ol!>IC22%!#<7$$!2E6\%\^q(e"!#;$"2b()3b][H7%!#<7$$!2Lk!>?N&He"!#;$"1oN4)zk/<%!#;7$$!0y%)4]2zd"!#9$"/A:!*\#4A%!#97$$!2_8;%zI)Hd"!#;$"2wkQe?p,F%!#<7$$!2h'R[a\kn:!#;$"2/Mg^X]NK%!#<7$$!16'fA*f-j:!#:$"1"*QSx+upV!#;7$$!2&\;AY4sd:!#;$"11NyP0zAW!#;7$$!20\]S#Rt_:!#;$"1'4&\f2msW!#;7$$!2e#\2r]zZ:!#;$"2Ou]#*G\?_%!#<7$$!2.#\?*G_Ga"!#;$"2wz]z5x9d%!#<7$$!1%)=dk4"y`"!#:$"0;"Ga.*=i%!#:7$$!2;9;\CnC`"!#;$"1&eQ3bF`n%!#;7$$!2m*oExvcF:!#;$"1L5LFUKCZ!#;7$$!20")\h(4tA:!#;$"1&*=]Q-psZ!#;7$$!2n*f:H2c<:!#;$"1M+W3FRC[!#;7$$!2@(zLP<S7:!#;$"1y-iEE)f([!#;7$$!1Fs"eBrx]"!#:$"1Hx#=k(GA\!#;7$$!1Lg%G2'G-:!#:$"0nR:FRr(\!#:7$$!2'*\KGM'p(\"!#;$"10]nrl.B]!#;7$$!2ZK^!Q"GB\"!#;$"1an[>'=n2&!#;7$$!2e-Nmq/s["!#;$"1V(\O$H&z7&!#;7$$!2@_^E4IE["!#;$"1zZ[t!*pt^!#;7$$!298$yga[x9!#;$"1&oo@RX^A&!#;7$$!2Y@bps1BZ"!#;$"1ayWIF$pF&!#;7$$!27>Xng_rY"!#;$"1)3[D$RZG`!#;7$$!2$)=Pv2uBY"!#;$"1="GYAfiP&!#;7$$!2_^Dt=EuX"!#;$"0&[uE"QdU&!#:7$$!2Fd!>s!4BX"!#;$"1uU4y#4pZ&!#;7$$!2`w3xO3sW"!#;$"1ZB"HK;z_&!#;7$$!0&H>m;'>W"!#9$"1,02QLQ!e&!#;7$$!23)>ko.MP9!#;$"1#>!e8jfEc!#;7$$!2s$4:#)y8K9!#;$"0j!\y6iyc!#:7$$!1<0vLS"pU"!#:$"1H[\i'f3t&!#;7$$!2=9hy))z=U"!#;$"1$e)Q@6?"y&!#;7$$!2Uz86S3tT"!#;$"1e?')))f"p#e!#;7$$!2G`27Ys=T"!#;$"1sY#zQv7)e!#;7$$!2$=N22vE29!#;$"1<[EH\KFf!#;7$$!21@%o]3">S"!#;$"1&*y:$\"*3)f!#;7$$!2%y"H@IprR"!#;$"1;#3(ypIGg!#;7$$!2&)Gp=2n>R"!#;$"1:rI"GH.3'!#;7$$!1#eT%=L,(Q"!#:$"1"=%e:o')Hh!#;7$$!2-jAkfW=Q"!#;$"1*ptd.a:='!#;7$$!2N%)3h4)4x8!#;$"1l:"*Q!>!Hi!#;7$$!2\]!Ha$y>P"!#;$"1^\4dk@!G'!#;7$$!1w%=9QgmO"!#:$"1T_"e='RLj!#;7$$!2RB+/2J?O"!#;$"1jw*fH*ozj!#;7$$!18kn(GJqN"!#:$"0(eBBroHk!#:7$$!2[h$*G-m=N"!#;$"1_Q1r(R8['!#;7$$!2AW9!>G"oM"!#;$"1yb&)4=(=`'!#;7$$!20WIWeB>M"!#;$"1&f&pbTw!e'!#;7$$!2Ne;I#\\O8!#;$"1nT$)p20Nm!#;7$$!2Cw'GHqhJ8!#;$"1wB82(HQo'!#;7$$!14YcO)3kK"!#:$"0"RNM;"ft'!#:7$$!2epo)R%*o@8!#;$"1WIJ,c5$y'!#;7$$!2B/CF*)HlJ"!#;$"1y&fF2,Z$o!#;7$$!2\$Q&4;v;J"!#;$"1a;Y!R[K)o!#;7$$!2CfEuc+mI"!#;$"1zStDV*R$p!#;7$$!2WY-ZAR;I"!#;$"1c`(Hv2O)p!#;7$$!2Xhj'e^W'H"!#;$"1dQO8%[b.(!#;7$$!23")QdlU9H"!#;$"1#*=hUMd&3(!#;7$$!2<pqR(oK'G"!#;$"1%3$Hg7tOr!#;7$$!2_^eMX`7G"!#;$"1[[TlaY(=(!#;7$$!2k*G"p]"fw7!#;$"1R5(3$\3Ms!#;7$$!2$>72!R[7F"!#;$"12yG*4;vG(!#;7$$!2XEsEWpkE"!#;$"1ctFtbINt!#;7$$!2&4%*)z3u8E"!#;$"10f5?"fiQ(!#;7$$!2"4`S$=(\c7!#;$"14p%f;G]V(!#;7$$!2[[>w+#3^7!#;$"1_^!Q#*z"*[(!#;7$$!2(Q^GjGRY7!#;$"18'[rOrg`(!#;7$$!2hpBDkq5C"!#;$"1RIwuNH*e(!#;7$$!2%*3!3;+AO7!#;$"13"*>R)*zPw!#;7$$!2#4s0$>94B"!#;$"13zUp!e3p(!#;7$$!2Q)Q5lhLE7!#;$"1i6'*[$Qmt(!#;7$$!12"[cKA6A"!#:$"0$*=Nuw()y(!#:7$$!2&3189g3;7!#;$"1:Rpe)R"Ry!#;7$$!2ie8F*H067!#;$"1QT'G2q%*)y!#;7$$!2`Iuo[Qg?"!#;$"0&pDJ^hRz!#:7$$!2nL6m6@7?"!#;$"1Lm)Q$))y()z!#;7$$!2liy<T8g>"!#;$"1NP@#)e')R!)!#;7$$!2Vdm94]5>"!#;$"1dUL&3*\*3)!#;7$$!2(*e`0VEe="!#;$"1.TY%pN<9)!#;7$$!2F9O&fx4"="!#;$"1u&QYSA!*=)!#;7$$!1$GWGpre<"!#:$"1srbrIGT#)!#;7$$!2m/G;.m3<"!#;$"1M&>PoR8H)!#;7$$!168LaD(e;"!#:$"0*oocWFT$)!#:7$$!1w3%z%olg6!#:$"0C"f?:V$R)!#:7$$!1c"\>*H&e:"!#:$"1T%303q9W)!#;7$$!2E75j=L4:"!#;$"1u()*o8o1\)!#;7$$!2yK.j8,b9"!#;$"1An'pj))\a)!#;7$$!2Wwg*fGeS6!#;$"1cBR+9<%f)!#;7$$!1#yc6+`b8"!#:$"1"=K%))*pWk)!#;7$$!1#G8VwP/8"!#:$"1"=noNAcp)!#;7$$!2\Wgi'etD6!#;$"1^bRP8kU()!#;7$$!2Q,&>&zB27"!#;$"1i)\![?w#z)!#;7$$!2GLSj()\d6"!#;$"1tmfO7]U))!#;7$$!2(=sCH$H/6"!#;$"18y_2nq&*))!#;7$$!1rH#p<Md5"!#:$"1#Hq2BeE%*)!#;7$$!2(H0"e%pJ+6!#;$"1.Z*=aIo**)!#;7$$!2BI#Q7$Ga4"!#;$"1xp<worX!*!#;7$$!2mcM^E"f!4"!#;$"1MVl[t3%4*!#;7$$!2QVFa))*Q&3"!#;$"1icsX65Y"*!#;7$$!2L?n]Yn,3"!#;$"1nzK\`K)>*!#;7$$!2Qt3e$eTv5!#;$"1iE">kTeC*!#;7$$!23(Gg;)p.2"!#;$"1$HrR$=I'H*!#;7$$!2iAM]RXa1"!#;$"1Qxl\gaX$*!#;7$$!2m0-,F2,1"!#;$"1M%z*)HF*)R*!#;7$$!1-x(yI)[b5!#:$"1")HA@p6X%*!#;7$$!2-uR=E$=]5!#;$"/Eg"Qn")\*!#97$$!1"eo'Ri>X5!#:$"0>9LgP![&*!#:7$$!2j,$p'Qd-/"!#;$"1P)pI8Euf*!#;7$$!24,B[g9`."!#;$"1"*)p<&R&ok*!#;7$$!2[(**=!Gt-."!#;$"1`-5)>nsp*!#;7$$!2@BM0cH\-"!#;$"1zwl%R/2v*!#;7$$!2u)\)G*)H+-"!#;$"1E,:r5q*z*!#;7$$!1,zw"H$>:5!#:$"1))4K#3n![)*!#;7$$!2s3uZ/B+,"!#;$"1G"fAbp(**)*!#;7$$!2E1cH0k[+"!#;$"1w$R/Zf8&**!#;7$$!+/+++5!"*$"1%e;y&********!#;7dw7$$!1,++!)********!#;$"2/0xRyFA"G!#D7$$!1[!f*HRUZ**!#;$"2lm%4/qgd_!#>7$$!1G5%**yx;!**!#;$"1zu*e+@A$)*!#=7$$!1O80r9B])*!#;$"2mh'[*G&o(\"!#=7$$!1=]cKTW)z*!#;$"2L%)\Vneb,#!#=7$$!0ie-$H!pu*!#:$"1)z8upq4`#!#<7$$!0X()zj<"*p*!#:$"2.]D,iB)3I!#=7$$!1-GnN(Q'\'*!#;$"20)>FVEh.N!#=7$$!1$p=Ten%)f*!#;$"1xI")eTK:S!#<7$$!0f'4R0YZ&*!#:$"16T.4YRDX!#<7$$!1p&GP_$*\\*!#;$"2DJ9Fwk+0&!#=7$$!1CS.[0y[%*!#;$"1e(f'>X>7b!#<7$$!1"\:HobnR*!#;$"2w4X3<VC.'!#=7$$!1LBq)><XM*!#;$"1mm(H,G[b'!#<7$$!1<sgRd<%H*!#;$"1Ry#RgU#eq!#<7$$!1")3&>(3Y[#*!#;$"0>"\!G"R:v!#;7$$!0$3ns95%>*!#:$"1-<Ht_)*e!)!#<7$$!1'[Y6$>0["*!#;$"1O^`)o![>&)!#<7$$!1X"RqO&[%4*!#;$"1a&3'Hj9b!*!#<7$$!1e"*H"))pq/*!#;$"1@%3q=,$H&*!#<7$$!1s@\yv/&**)!#;$"2w#y]@C&\+"!#<7$$!1bp,W+^X*)!#;$"2X/$)f&**[a5!#<7$$!0p?O#G#Q*))!#:$"20Jzj<xh5"!#<7$$!1iHH?yNY))!#;$"2%Qqqz@k`6!#<7$$!1'y/>Sg^z)!#;$"2[@&4)fR[?"!#<7$$!1w<(Hn!)>u)!#;$"2OAGqK>!e7!#<7$$!1&=/Ec(o&p)!#;$"2["eRPCJ/8!#<7$$!1')f;N(*oX')!#;$"2W,M[E5VN"!#<7$$!0RJr3PSf)!#:$"2'4'oG"H'fS"!#<7$$!1Rv8[]]V&)!#;$"2:Yi=&\\c9!#<7$$!1^>5-Fh%\)!#;$"2([!)*yH(Q0:!#<7$$!1Miu(3E.W)!#;$"2nw`A"Rnf:!#<7$$!12HD]ra"R)!#;$"2C4Z(\GX3;!#<7$$!1WI#GAl%R$)!#;$"2u&p<xZ`g;!#<7$$!1P^nb7F#H)!#;$"1j[KW(Gxq"!#;7$$!1AA-%yv1C)!#;$"2sxxf@C$f<!#<7$$!0'f7m%G@>)!#:$"2./uQ`ry!=!#<7$$!0b]1`#QT")!#:$"0X\$puhe=!#:7$$!193@."p<4)!#;$"2`=*y'*3B3>!#<7$$!1cXhU%G)R!)!#;$"2XW&Qd:<g>!#<7$$!1:k;8M!)*)z!#;$"2ZeLoe'>5?!#<7$$!1$f!G&fX'Qz!#;$"12%>ZSa81#!#;7$$!1$*e&**Q6z)y!#;$"2y5W+h)37@!#<7$$!1DKJC>HTy!#;$"2bx'ov!3(e@!#<7$$!1GFob2'yy(!#;$"2AF<VCR@@#!#<7$$!1F?]"Gr+u(!#;$"2W(z\=(G*fA!#<7$$!0mpWt<"*o(!#:$"2'R.`lA)3J#!#<7$$!0eL%)o[.k(!#:$"2.Um:J^'fB!#<7$$!1J(e.$p>'e(!#;$"2$p7kpI!QT#!#<7$$!1.x#o[0$Rv!#;$"1)HsJ^%pgC!#;7$$!1"R+!zK3'[(!#;$"14'**4s;R^#!#;7$$!1'HqV,xvV(!#;$"1/(Hc)HUiD!#;7$$!1h#HRy=XQ(!#;$"2'Q22;7[:E!#<7$$!1')G@/&Q(Qt!#;$"2X6(y&\h7m#!#<7$$!1llW4,g'G(!#;$"1NMb!*)*R8F!#;7$$!1H,2%*pBOs!#;$"1s)Hf+jPw#!#;7$$!1%e)pzn!f=(!#;$"1;9I?K49G!#;7$$!1&>06shd8(!#;$"10[*)y#QU'G!#;7$$!19GG=!)e(3(!#;$"2c=<<)>T7H!#<7$$!1/uup4^Nq!#;$"1(f_-.*[kH!#;7$$!1\$Gkwxe)p!#;$"2<lrNBAT,$!#<7$$!1c&*3d6kLp!#;$"2WW5H%)ej1$!#<7$$!0%fsYWN')o!#:$"2:1uKbXO6$!#<7$$!1*H)fzP4Mo!#;$"1,<S?i!f;$!#;7$$!16dBnr.%y'!#;$"1*GkF$G'f@$!#;7$$!1;'oSR-Tt'!#;$"2VQJfg(*eE$!#<7$$!1Oc&*H`%>o'!#;$"2ZOW+na!=L!#<7$$!1$GY)pn!Rj'!#;$"1<P:IK4mL!#;7$$!1b"fKr3Ze'!#;$"2Z%3u'G"H:M!#<7$$!1DR(H@)QIl!#;$"2c2Eqy6'pM!#<7$$!1h:N\a?"['!#;$"1Q%[1b%z=N!#;7$$!1W06ho!4V'!#;$"2wX*))QJ4pN!#<7$$!1L4Z#\a(zj!#;$"2u1Hv]X-i$!#<7$$!1'[a<^NFL'!#;$"2Z^X#)[ksm$!#<7$$!1$p**3![h#G'!#;$"12.5*>&Q<P!#;7$$!1DR:7c(GB'!#;$"1vg%yQCrw$!#;7$$!1j*459q'zh!#;$"1P+**e)H.#Q!#;7$$!0ozvh=F8'!#:$"21K?CQ"GnQ!#<7$$!1z&QiIY&yg!#;$"1@9w$p`9#R!#;7$$!1e2wr*f'Hg!#;$"2ECR#G+MqR!#<7$$!1=**3*\*G")f!#;$"1#354]5(=S!#;7$$!1P0"=qv#Hf!#;$"1j%*=)HC22%!#;7$$!1L$**z\^q(e!#;$"2tm+?][H7%!#<7$$!1uXA0_`He!#;$"2kUvZzk/<%!#<7$$!1-T'H,v!zd!#;$"1)*e.()\#4A%!#;7$$!1x13(zI)Hd!#;$"1B$>H?p,F%!#;7$$!1faaZ&\kn&!#;$"1TXX_/bBV!#;7$$!1^r6D*f-j&!#;$"2&[G)[2S(pV!#<7$$!1N`_k%4sd&!#;$"1mYZN0zAW!#;7$$!1iUhU#Rt_&!#;$"2&QdQd2msW!#<7$$!1i5m72&zZ&!#;$"2%Q*QtG\?_%!#<7$$!1(HjP*G_Ga!#;$"1/nB1rZrX!#;7$$!1"GJsk4"y`!#;$"2%>(oFN!*=i%!#<7$$!10,Y]CnC`!#;$"1&*)R&\vKvY!#;7$$!0nrPxvcF&!#:$"0LGiACVs%!#:7$$!1XtSi(4tA&!#;$"1bEfP-psZ!#;7$$!1'RiAH2c<&!#;$"1/wt2FRC[!#;7$$!1"zvQP<S7&!#;$"2&4U7EE)f([!#<7$$!1@J[eBrx]!#;$"1zo^TwGA\!#;7$$!1t<bG2'G-&!#;$"2lA[9FRr(\!#<7$$!1^GBGM'p(\!#;$"1\rwrl.B]!#;7$$!2NP1-Q"GB\!#<$"1EOz>'=n2&!#;7$$!1X%Qe1Z?([!#;$"1b:;MH&z7&!#;7$$!1E/#e#4IE[!#;$"1u&zT2*pt^!#;7$$!1L2$pga[x%!#;$"1n#pIRX^A&!#;7$$!1:WWos1BZ!#;$"1&eb:tKpF&!#;7$$!2l,Qh1E:n%!#<$"1%)>'Q$RZG`!#;7$$!1Zo'QxSPi%!#;$"1`J8E#fiP&!#;7$$!/Abr=EuX!#9$"/yWG"QdU&!#97$$!1"4)**>24BX!#;$"14>+!G4pZ&!#;7$$!2&))f(\n$3sW!#<$"17S-Dj"z_&!#;7$$!2n'zgfmh>W!#<$"1L?RSLQ!e&!#;7$$!2;U8Ro.MP%!#<$"1yl3;jfEc!#;7$$!2w)[z=)y8K%!#<$"17^?"=@'yc!#;7$$!29t"eM.9pU!#<$"1p#=amf3t&!#;7$$!2Yh'[v))z=U!#<$"1&Q8X7,7y&!#;7$$!1y-$y+%3tT!#;$"1A(p@*f"p#e!#;7$$!1G-b3Ys=T!#;$"1s(\9Rv7)e!#;7$$!1%)e-n]nsS!#;$"1;T(H$\KFf!#;7$$!29a=H]3">S!#<$"1f93(\"*3)f!#;7$$!1c&yr,$prR!#;$"1W9#G)pIGg!#;7$$!1p:P92n>R!#;$"1J%GcGH.3'!#;7$$!2BN'*)zJ8qQ!#<$"1[O5?o')Hh!#;7$$!2k3+&ffW=Q!#<$"19**\SSb"='!#;7$$!2%eB<c4)4x$!#<$"1Uw#Q/>!Hi!#;7$$!2E=%yPNy>P!#<$"1<e@ik@!G'!#;7$$!1t6&)3QgmO!#;$"1F)[6>'RLj!#;7$$!1#e$[)p5.i$!#;$"1=k^,$*ozj!#;7$$!2CQX5(GJqN!#<$"1=Y&*GroHk!#;7$$!1)y5IAg'=N!#;$"17#*)pxR8['!#;7$$!2`$p,%=G"oM!#<$"1lI)f"=(=`'!#;7$$!1\8)z$eB>M!#;$"1^'=?;k2e'!#;7$$!21jDOA\\O$!#<$"1pVPw20Nm!#;7$$!10B8'GqhJ$!#;$"1&pnQrHQo'!#;7$$!2;W-(e$)3kK!#<$"1evHT;"ft'!#;7$$!2X`a:R%*o@$!#<$"1maW3c5$y'!#;7$$!0i,*>*)HlJ!#:$"0Q)4!3,Z$o!#:7$$!2aN0?g^n6$!#<$"1XY*zR[K)o!#;7$$!2t%*Hlm0g1$!#<$"1`+ZLV*R$p!#;7$$!16-4RAR;I!#;$"1*y44w2O)p!#;7$$!1`R\y:XkH!#;$"1Zg]@%[b.(!#;7$$!17e/\lU9H!#;$"1)=a4Xtb3(!#;7$$!2D**f6toK'G!#<$"13+%)o7tOr!#;7$$!2'*GNe_MD"G!#<$"0rkTZlu=(!#:7$$!1BE>g]"fw#!#;$"1xt!)R\3Ms!#;7$$!2j7i:*Q[7F!#<$"1uyV3h^(G(!#;7$$!2NU"Q<WpkE!#<$"1w&=Ee0`L(!#;7$$!2$e!\.(3u8E!#<$"1V4lH"fiQ(!#;7$$!1xHJC=(\c#!#;$"1Bqov"G]V(!#;7$$!2v7Qi1?3^#!#<$"1t=wL*z"*[(!#;7$$!1,rqA'GRY#!#;$"1**GHx82Ov!#;7$$!2&)yz[T12T#!#<$"16-7&e$H*e(!#;7$$!2Pp\-:+AO#!#<$"11.v\)*zPw!#;7$$!20m3)>>94B!#<$"0M">!3e3p(!#:7$$!1$G#4S;OjA!#;$"1<x!*f$Qmt(!#;7$$!2G'fKXKA6A!#<$"1QSnanx)y(!#;7$$!2c_\*H,'3;#!#<$"1u/0q)R"Ry!#;7$$!2A)zd:*H06#!#<$"1>?U%3q%*)y!#;7$$!2Gf%)p&[Qg?!#<$"13a,V^hRz!#;7$$!27@iT:6A,#!#<$"1*yPe%))y()z!#;7$$!22!oi0T8g>!#<$"1*>tV*e')R!)!#;7$$!2du2B!4]5>!#<$"1aAp(4*\*3)!#;7$$!1`*oHHk#e=!#;$"1[5.2dtT")!#;7$$!2lL0Eex4"=!#<$"1kYR<C-*=)!#;7$$!2spxa"pre<!#<$"1.B_%3$GT#)!#;7$$!2#3^6..m3<!#<$"1#*[)opR8H)!#;7$$!18![*Hbse;!#;$"1()>0qWFT$)!#;7$$!2V.NeYolg"!#<$"1m\;M:V$R)!#;7$$!22oDd!*H&e:!#<$"1>VF%4q9W)!#;7$$!2KbQ"\=L4:!#<$"1Z9'3:o1\)!#;7$$!2MK`)[8,b9!#<$"1xm9^'))\a)!#;7$$!1d4B&eGeS"!#;$"1V!pZTrTf)!#;7$$!2:%**)p**HbN"!#<$"1f+,.+ZW')!#;7$$!2%H.NGwP/8!#<$"1s'\;PAcp)!#;7$$!2F)QjZ'etD"!#<$"1=hO_8kU()!#;7$$!2(*3zn$zB27!#<$"0"4Aj?w#z)!#:7$$!2@KL![()\d6!#<$"1zm'>D,D%))!#;7$$!1h$*)oF$H/6!#;$"1R16Bnq&*))!#;7$$!2o2fMvTt0"!#<$"1C4aY#eE%*)!#;7$$!1wz6U%pJ+"!#;$"1D?)ybIo**)!#;7$$!1[:Sw5$Ga*!#<$"1X)fB*orX!*!#;7$$!1ZJp\j7f!*!#<$"1&oI]O(3%4*!#;7$$!1E$**oP))*Q&)!#<$"1n+Ji65Y"*!#;7$$!1&H(yQju;!)!#<$"0F@hOD$)>*!#:7$$!1)pR5T$eTv!#<$"0.'*)e;%eC*!#:7$$!1,]V)[")p.(!#<$"/l:^=I'H*!#97$$!1^2gH$RXa'!#<$"1D*Rq1YbM*!#;7$$!1f&[U$os5g!#<$"1V^d;t#*)R*!#;7$$!1%\l*41$)[b!#<$"1^M+Rp6X%*!#;7$$!18t//gK=]!#<$"1o_f*Rn")\*!#;7$$!1)eO\yB'>X!#<$"1Uj]@w.[&*!#;7$$!1%e/a[Qd-%!#<$"1U&f9:Euf*!#;7$$!1OpU'Hg9`$!#<$"13tNqR&ok*!#;7$$!2`y16$yKFI!#=$"1@$*)o@nsp*!#;7$$!0.&Rje&H\#!#;$"1)\gOT/2v*!#;7$$!2cm5l4*)H+#!#=$"1L*[.4,(*z*!#;7$$!2%=u'G)*G$>:!#=$"0E8<5n![)*!#:7$$!21#zT"G/B+"!#=$"0@e=dp(**)*!#:7$$!2l*)=b(40k[!#>$"0"[C!\f8&**!#:7$$!#?!#5$"1Ax(=(********!#;7dw7$$"#?!#5$"1**eYGxA7G!#C7$$"13_4/qgd_!#=$"2lm%4/qgd_!#>7$$"1bs*e+@A$)*!#=$"1Cu*e+@A$)*!#=7$$"2mk'[*G&o(\"!#=$"0l'[*G&o(\"!#;7$$"2j#)\Vneb,#!#=$"2L%)\Vneb,#!#=7$$"11QT(pq4`#!#<$"14QT(pq4`#!#<7$$"0^D,iB)3I!#;$"1<b7?O#)3I!#<7$$"1#)>FVEh.N!#<$"20)>FVEh.N!#=7$$"1wI")eTK:S!#<$"1$38)eTK:S!#<7$$"/T.4YRDX!#:$"/T.4YRDX!#:7$$"2YJ9Fwk+0&!#=$"2DJ9Fwk+0&!#=7$$"1l(f'>X>7b!#<$"1e(f'>X>7b!#<7$$"2D5X3<VC.'!#=$"2w4X3<VC.'!#=7$$"1om(H,G[b'!#<$"1rm(H,G[b'!#<7$$"1Ny#RgU#eq!#<$"1Ly#RgU#eq!#<7$$"1*>"\!G"R:v!#<$"1-7\!G"R:v!#<7$$"1(p"Ht_)*e!)!#<$"1"p"Ht_)*e!)!#<7$$"1V^`)o![>&)!#<$"1U^`)o![>&)!#<7$$"0c3'Hj9b!*!#;$"0c3'Hj9b!*!#;7$$"1A%3q=,$H&*!#<$"1@%3q=,$H&*!#<7$$"2'Gy]@C&\+"!#<$"2(Gy]@C&\+"!#<7$$"2_/$)f&**[a5!#<$"1XI)f&**[a5!#;7$$"29Jzj<xh5"!#<$"16$zj<xh5"!#;7$$"2%Rqqz@k`6!#<$"2&Rqqz@k`6!#<7$$"2W@&4)fR[?"!#<$"2[@&4)fR[?"!#<7$$"2UAGqK>!e7!#<$"2OAGqK>!e7!#<7$$"2c"eRPCJ/8!#<$"2a"eRPCJ/8!#<7$$"2_,M[E5VN"!#<$"2W,M[E5VN"!#<7$$"20hoG"H'fS"!#<$"2-hoG"H'fS"!#<7$$"2BYi=&\\c9!#<$"1iC'=&\\c9!#;7$$"2([!)*yH(Q0:!#<$"2([!)*yH(Q0:!#<7$$"2nw`A"Rnf:!#<$"2nw`A"Rnf:!#<7$$"1$4Z(\GX3;!#;$"2C4Z(\GX3;!#<7$$"2j&p<xZ`g;!#<$"2d&p<xZ`g;!#<7$$"2P'[KW(Gxq"!#<$"1k[KW(Gxq"!#;7$$"2'yx(f@C$f<!#<$"1zx(f@C$f<!#;7$$"26/uQ`ry!=!#<$"29/uQ`ry!=!#<7$$"2)\%\$puhe=!#<$"0X\$puhe=!#:7$$"2n=*y'*3B3>!#<$"2k=*y'*3B3>!#<7$$"2UW&Qd:<g>!#<$"1WaQd:<g>!#;7$$"2beLoe'>5?!#<$"2`eLoe'>5?!#<7$$"2mS>ZSa81#!#<$"11%>ZSa81#!#;7$$"13T/5')37@!#;$"2y5W+h)37@!#<7$$"2ex'ov!3(e@!#<$"2bx'ov!3(e@!#<7$$"2AF<VCR@@#!#<$"2AF<VCR@@#!#<7$$"2O(z\=(G*fA!#<$"2L(z\=(G*fA!#<7$$"2-MIbE#)3J#!#<$"2'R.`lA)3J#!#<7$$"2(>kc68lfB!#<$"2(>kc68lfB!#<7$$"2-FT'pI!QT#!#<$"2/FT'pI!QT#!#<7$$"1(HsJ^%pgC!#;$"2oHsJ^%pgC!#<7$$"2%4'**4s;R^#!#<$"14'**4s;R^#!#;7$$"10(Hc)HUiD!#;$"10(Hc)HUiD!#;7$$"2'Q22;7[:E!#<$"2'Q22;7[:E!#<7$$"2X6(y&\h7m#!#<$"19ry&\h7m#!#;7$$"2dV`0*)*R8F!#<$"1NMb!*)*R8F!#;7$$"2B()Hf+jPw#!#<$"2B()Hf+jPw#!#<7$$"2jT,.A$49G!#<$"2jT,.A$49G!#<7$$"2c![*)y#QU'G!#<$"2c![*)y#QU'G!#<7$$"1'=<<)>T7H!#;$"2c=<<)>T7H!#<7$$"2nf_-.*[kH!#<$"1'f_-.*[kH!#;7$$"2<lrNBAT,$!#<$"2<lrNBAT,$!#<7$$"1W/"H%)ej1$!#;$"1W/"H%)ej1$!#;7$$"1hSF`bk8J!#;$"1hSF`bk8J!#;7$$"28q,/A1f;$!#<$"28q,/A1f;$!#<7$$"1*GkF$G'f@$!#;$"2')GkF$G'f@$!#<7$$"2VQJfg(*eE$!#<$"2VQJfg(*eE$!#<7$$"1kV/qY0=L!#;$"2OOW+na!=L!#<7$$"1<P:IK4mL!#;$"1<P:IK4mL!#;7$$"2Z%3u'G"H:M!#<$"2Z%3u'G"H:M!#<7$$"1vg-(y6'pM!#;$"2X2Eqy6'pM!#<7$$"2(R%[1b%z=N!#<$"2(R%[1b%z=N!#<7$$"2lX*))QJ4pN!#<$"1c%*))QJ4pN!#;7$$"1o!Hv]X-i$!#;$"2u1Hv]X-i$!#<7$$"1:bC)[ksm$!#;$"1:bC)[ksm$!#;7$$"13.5*>&Q<P!#;$"13.5*>&Q<P!#;7$$"1vg%yQCrw$!#;$"1vg%yQCrw$!#;7$$"2v.!**e)H.#Q!#<$"2v.!**e)H.#Q!#<7$$"1@.U#Q"GnQ!#;$"1@.U#Q"GnQ!#;7$$"1@9w$p`9#R!#;$"1@9w$p`9#R!#;7$$"2ECR#G+MqR!#<$"1U#R#G+MqR!#;7$$"2E354]5(=S!#<$"2E354]5(=S!#<7$$"1k%*=)HC22%!#;$"1k%*=)HC22%!#;7$$"2%o1+-&[H7%!#<$"2%o1+-&[H7%!#<7$$"1Fax%zk/<%!#;$"1Fax%zk/<%!#;7$$"2%)*e.()\#4A%!#<$"1)*e.()\#4A%!#;7$$"2LK>H?p,F%!#<$"2LK>H?p,F%!#<7$$"2:aaCX]NK%!#<$"2:aaCX]NK%!#<7$$"2&[G)[2S(pV!#<$"2&[G)[2S(pV!#<7$$"2mmua`!zAW!#<$"2mmua`!zAW!#<7$$"2&QdQd2msW!#<$"1QdQd2msW!#;7$$"2%Q*QtG\?_%!#<$"2%Q*QtG\?_%!#<7$$"2VqOi5x9d%!#<$"2VqOi5x9d%!#<7$$"0soFN!*=i%!#:$"0soFN!*=i%!#:7$$"2b*)R&\vKvY!#<$"2b*)R&\vKvY!#<7$$"1J$GiACVs%!#;$"0LGiACVs%!#:7$$"2bl#fP-psZ!#<$"2bl#fP-psZ!#<7$$"10wt2FRC[!#;$"1/wt2FRC[!#;7$$"0@Chi#)f([!#:$"2&4U7EE)f([!#<7$$"0)o^TwGA\!#:$"0)o^TwGA\!#:7$$"1F#[9FRr(\!#;$"1F#[9FRr(\!#;7$$"0:n<dOI-&!#:$"0:n<dOI-&!#:7$$"1GOz>'=n2&!#;$"1GOz>'=n2&!#;7$$"1c:;MH&z7&!#;$"1c:;MH&z7&!#;7$$"1v&zT2*pt^!#;$"1v&zT2*pt^!#;7$$"1o#pIRX^A&!#;$"1o#pIRX^A&!#;7$$"1'eb:tKpF&!#;$"1'eb:tKpF&!#;7$$"1&)>'Q$RZG`!#;$"1&)>'Q$RZG`!#;7$$"1aJ8E#fiP&!#;$"1aJ8E#fiP&!#;7$$"1,yWG"QdU&!#;$"1,yWG"QdU&!#;7$$"0">+!G4pZ&!#:$"0">+!G4pZ&!#:7$$"18S-Dj"z_&!#;$"18S-Dj"z_&!#;7$$"1M?RSLQ!e&!#;$"1M?RSLQ!e&!#;7$$"0e'3;jfEc!#:$"0e'3;jfEc!#:7$$"18^?"=@'yc!#;$"18^?"=@'yc!#;7$$"0F=amf3t&!#:$"0F=amf3t&!#:7$$"1(Q8X7,7y&!#;$"1(Q8X7,7y&!#;7$$"1B(p@*f"p#e!#;$"1B(p@*f"p#e!#;7$$"1t(\9Rv7)e!#;$"1t(\9Rv7)e!#;7$$"1<T(H$\KFf!#;$"1<T(H$\KFf!#;7$$"0Y"3(\"*3)f!#:$"0Y"3(\"*3)f!#:7$$"1X9#G)pIGg!#;$"1X9#G)pIGg!#;7$$"1K%GcGH.3'!#;$"1K%GcGH.3'!#;7$$"1\O5?o')Hh!#;$"1\O5?o')Hh!#;7$$"1:**\SSb"='!#;$"1:**\SSb"='!#;7$$"1Vw#Q/>!Hi!#;$"1Vw#Q/>!Hi!#;7$$"1>e@ik@!G'!#;$"1>e@ik@!G'!#;7$$"1G)[6>'RLj!#;$"1G)[6>'RLj!#;7$$"1>k^,$*ozj!#;$"1>k^,$*ozj!#;7$$"1>Y&*GroHk!#;$"1>Y&*GroHk!#;7$$"18#*)pxR8['!#;$"17#*)pxR8['!#;7$$"1mI)f"=(=`'!#;$"1mI)f"=(=`'!#;7$$"1_'=?;k2e'!#;$"1_'=?;k2e'!#;7$$"0Pujx]]j'!#:$"0Pujx]]j'!#:7$$"1'pnQrHQo'!#;$"1&pnQrHQo'!#;7$$"0c(HT;"ft'!#:$"1hvHT;"ft'!#;7$$"1naW3c5$y'!#;$"1naW3c5$y'!#;7$$"1"Q)4!3,Z$o!#;$"1"Q)4!3,Z$o!#;7$$"1YY*zR[K)o!#;$"1XY*zR[K)o!#;7$$"1a+ZLV*R$p!#;$"1`+ZLV*R$p!#;7$$"0z44w2O)p!#:$"1*y44w2O)p!#;7$$"1[g]@%[b.(!#;$"1[g]@%[b.(!#;7$$"1*=a4Xtb3(!#;$"1*=a4Xtb3(!#;7$$"14+%)o7tOr!#;$"14+%)o7tOr!#;7$$"16Z;uaY(=(!#;$"0rkTZlu=(!#:7$$"1yt!)R\3Ms!#;$"1yt!)R\3Ms!#;7$$"1vyV3h^(G(!#;$"1vyV3h^(G(!#;7$$"1y&=Ee0`L(!#;$"1y&=Ee0`L(!#;7$$"1V4lH"fiQ(!#;$"1V4lH"fiQ(!#;7$$"1Cqov"G]V(!#;$"1Cqov"G]V(!#;7$$"1u=wL*z"*[(!#;$"1u=wL*z"*[(!#;7$$"/HHx82Ov!#9$"1**GHx82Ov!#;7$$"18-7&e$H*e(!#;$"16-7&e$H*e(!#;7$$"12.v\)*zPw!#;$"11.v\)*zPw!#;7$$"1T8>!3e3p(!#;$"0M">!3e3p(!#:7$$"1=x!*f$Qmt(!#;$"1<x!*f$Qmt(!#;7$$"1QSnanx)y(!#;$"1QSnanx)y(!#;7$$"1w/0q)R"Ry!#;$"1w/0q)R"Ry!#;7$$"1>?U%3q%*)y!#;$"1>?U%3q%*)y!#;7$$"13a,V^hRz!#;$"13a,V^hRz!#;7$$"0zPe%))y()z!#:$"1*yPe%))y()z!#;7$$"/KP%*e')R!)!#9$"1*>tV*e')R!)!#;7$$"1bAp(4*\*3)!#;$"1aAp(4*\*3)!#;7$$"1[5.2dtT")!#;$"1[5.2dtT")!#;7$$"1lYR<C-*=)!#;$"1lYR<C-*=)!#;7$$"1/B_%3$GT#)!#;$"1/B_%3$GT#)!#;7$$"1$*[)opR8H)!#;$"1#*[)opR8H)!#;7$$"1))>0qWFT$)!#;$"1()>0qWFT$)!#;7$$"1n\;M:V$R)!#;$"1o\;M:V$R)!#;7$$"0KuU4q9W)!#:$"0KuU4q9W)!#:7$$"1[9'3:o1\)!#;$"1[9'3:o1\)!#;7$$"1ym9^'))\a)!#;$"1zm9^'))\a)!#;7$$"1W!pZTrTf)!#;$"1W!pZTrTf)!#;7$$"015I+qWk)!#:$"1h+,.+ZW')!#;7$$"1s'\;PAcp)!#;$"1s'\;PAcp)!#;7$$"1=hO_8kU()!#;$"1=hO_8kU()!#;7$$"164Aj?w#z)!#;$"164Aj?w#z)!#;7$$"1zm'>D,D%))!#;$"1zm'>D,D%))!#;7$$"0k5Js1d*))!#:$"1T16Bnq&*))!#;7$$"1C4aY#eE%*)!#;$"1C4aY#eE%*)!#;7$$"1D?)ybIo**)!#;$"1D?)ybIo**)!#;7$$"1Y)fB*orX!*!#;$"1Z)fB*orX!*!#;7$$"1'oI]O(3%4*!#;$"1&oI]O(3%4*!#;7$$"1p+Ji65Y"*!#;$"1p+Ji65Y"*!#;7$$"1s77m`K)>*!#;$"1s77m`K)>*!#;7$$"1Jg*)e;%eC*!#;$"0.'*)e;%eC*!#:7$$"1,l:^=I'H*!#;$"/l:^=I'H*!#97$$"1E*Rq1YbM*!#;$"1D*Rq1YbM*!#;7$$"1X^d;t#*)R*!#;$"1W^d;t#*)R*!#;7$$"1_M+Rp6X%*!#;$"1_M+Rp6X%*!#;7$$"0F&f*Rn")\*!#:$"1o_f*Rn")\*!#;7$$"1Uj]@w.[&*!#;$"1Uj]@w.[&*!#;7$$"1V&f9:Euf*!#;$"1V&f9:Euf*!#;7$$"13tNqR&ok*!#;$"13tNqR&ok*!#;7$$"1B$*)o@nsp*!#;$"1B$*)o@nsp*!#;7$$"1)\gOT/2v*!#;$"1)\gOT/2v*!#;7$$"1N*[.4,(*z*!#;$"1L*[.4,(*z*!#;7$$"1fKr,r1[)*!#;$"1fKr,r1[)*!#;7$$"14#e=dp(**)*!#;$"13#e=dp(**)*!#;7$$"17[C!\f8&**!#;$"1@[C!\f8&**!#;7$$"1,++!)********!#;$"1Ax(=(********!#;7dw7$$"+/+++5!"*$"1tK%\cT$=U!#C7$$"1lI)*3wD05!#:$"2&)4lI)*3wD&!#>7$$"2%ol'HAK)45!#;$"1#Qol'HAK)*!#=7$$"2"f\$[&o(\,"!#;$"1.f\$[&o(\"!#<7$$"1wGm)eb,-"!#:$"2ne(Gm)eb,#!#=7$$"2$**G()3(4`-"!#;$"2G"**G()3(4`#!#=7$$"2A!43Q#)3I5!#;$"23@!43Q#)3I!#=7$$"2bd#HGh.N5!#;$"2kad#HGh.N!#=7$$"2y^FMC`,/"!#;$"1k<vUVK:S!#<7$$"2_K4z%RDX5!#;$"18D$4z%RDX!#<7$$"239D%\1]]5!#;$"2`19D%\1]]!#=7$$"06wp%>7b5!#9$"1%)4h(p%>7b!#<7$$"2L:nMVC.1"!#;$"1F`rYLWKg!#<7$$"2Pdn=G[b1"!#;$"1htv'=G[b'!#<7$$"2([pvFCeq5!#;$"1i[pvFCeq!#<7$$"2lH/X"R:v5!#;$"1['H/X"R:v!#<7$$"2xb5W&)*e!3"!#;$"1sd0Ta)*e!)!#<7$$"2CdW&3[>&3"!#;$"1HsXa3[>&)!#<7$$"2*zQ$\Y^04"!#;$"1%*zQ$\Y^0*!#<7$$"2B"*)[8IH&4"!#;$"1G7*)[8IH&*!#<7$$"1-)[PC&\+6!#:$"2#>!)[PC&\+"!#<7$$"2(3l<(**[a5"!#;$"2d3l<(**[a5!#<7$$"2.Y&>>xh56!#;$"1-Y&>>xh5"!#;7$$"2sC4&>UO:6!#;$"2>Z#4&>UO:"!#<7$$"2deF8'R[?6!#;$"1ceF8'R[?"!#;7$$"2[h*>M>!e7"!#;$"2x9'*>M>!e7!#<7$$"2n&y@X7VI6!#;$"2acy@X7VI"!#<7$$"2vnTz-Ja8"!#;$"2Qx;%z-Ja8!#<7$$"1wWs#H'fS6!#:$"2#eZCFH'fS"!#<7$$"2$[Og'\\c9"!#;$"2B[Og'\\c9!#<7$$"0l(=J(Q0:"!#9$"/l(=J(Q0:!#97$$"2t],ERnf:"!#;$"2A2:g#Rnf:!#<7$$"1G8L'GX3;"!#:$"0G8L'GX3;!#:7$$"2=[`!zM0m6!#;$"2y"[`!zM0m"!#<7$$"1&R\d(Gxq6!#:$"2$\R\d(Gxq"!#<7$$"2#[S*GUKf<"!#;$"1"[S*GUKf<!#;7$$"2dDkY:(y!="!#;$"1cDkY:(y!=!#;7$$"2")\">[<'e="!#;$"1")\">[<'e=!#;7$$"2ji:44B3>"!#;$"2FEc"44B3>!#<7$$"1wW&p:<g>"!#:$"1fZap:<g>!#;7$$"0Gz)f'>5?"!#9$"2%*z#z)f'>5?!#<7$$"2))RZ;WNh?"!#;$"2s)RZ;WNh?!#<7$$"2adf@')37@"!#;$"1`df@')37@!#;7$$"2W>0(33(e@"!#;$"2P%>0(33(e@!#<7$$"2<(oaDR@@7!#;$"2eroaDR@@#!#<7$$"1Ee%H(G*fA"!#:$"2$f#e%H(G*fA!#<7$$"27oGwA)3J7!#;$"16oGwA)3J#!#;7$$"2;y7A8lfB"!#;$"1;y7A8lfB!#;7$$"2fg)*zI!QT7!#;$"2x0')*zI!QT#!#<7$$"2>&HL_%pgC"!#;$"1=&HL_%pgC!#;7$$"2WR%4t;R^7!#;$"1VR%4t;R^#!#;7$$"29+Q&*HUiD"!#;$"2E,!Q&*HUiD!#<7$$"28)3cA"[:E"!#;$"18)3cA"[:E!#;7$$"12U^]h7m7!#:$"2'p?90:EhE!#<7$$"2N)*p**)*R8F"!#;$"1N)*p**)*R8F!#;7$$"1#[([,jPw7!#:$"20#[([,jPw#!#<7$$"2X]/HK49G"!#;$"1X]/HK49G!#;7$$"2_yV(GQU'G"!#;$"1_yV(GQU'G!#;7$$"2Qv1!*>T7H"!#;$"1Qv1!*>T7H!#;7$$"1k%RQ!*[kH"!#:$"2wj%RQ!*[kH!#<7$$"2j^^TA79I"!#;$"1h^^TA79I!#;7$$"23]k])ej18!#;$"2&3]k])ej1$!#<7$$"2y%>3cXO68!#;$"1y%>3cXO6$!#;7$$"2y!QxA1f;8!#;$"1y!QxA1f;$!#;7$$"1W+*RG'f@8!#:$"1Q/!*RG'f@$!#;7$$"2%znGh(*eE8!#;$"1%znGh(*eE$!#;7$$"2Y@xwY0=L"!#;$"1X@xwY0=L!#;7$$"2X$*oOK4mL"!#;$"1V$*oOK4mL!#;7$$"2z'zIH"H:M"!#;$"2knzIH"H:M!#<7$$"1jZJz6'pM"!#:$"1Fw9$z6'pM!#;7$$"2hKdcXz=N"!#;$"1hKdcXz=N!#;7$$"2&38Y9$4pN"!#;$"2O38Y9$4pN!#<7$$"2'3[I^X-i8!#;$"2a3[I^X-i$!#<7$$"2ckd$\ksm8!#;$"2`XwN\ksm$!#<7$$"2o2B/_Q<P"!#;$"2`wIU?&Q<P!#<7$$"2xvx#RCrw8!#;$"2bdxFRCrw$!#<7$$"2=(3P')H.#Q"!#;$"1=(3P')H.#Q!#;7$$"2'>^pQ"GnQ"!#;$"2d>^pQ"GnQ!#<7$$"23c2)p`9#R"!#;$"2wgv!)p`9#R!#<7$$"2#)yNK+MqR"!#;$"1")yNK+MqR!#;7$$"2T_$[]5(=S"!#;$"1U_$[]5(=S!#;7$$"2ol!>IC229!#;$"2vc1>IC22%!#<7$$"2u)3b][H79!#;$"2W()3b][H7%!#<7$$"2nN4)zk/<9!#;$"1nN4)zk/<%!#;7$$"0A:!*\#4A9!#9$"1*>_,*\#4A%!#;7$$"2['Qe?p,F9!#;$"2lkQe?p,F%!#<7$$"2R.;b/bBV"!#;$"1R.;b/bBV!#;7$$"1*QSx+upV"!#:$"2(*)QSx+upV!#<7$$"20NyP0zAW"!#;$"10NyP0zAW!#;7$$"2&4&\f2msW"!#;$"1&4&\f2msW!#;7$$"2U2D*G\?_9!#;$"2Du]#*G\?_%!#<7$$"2(z]z5x9d9!#;$"2lz]z5x9d%!#<7$$"1;"Ga.*=i9!#:$"1f6Ga.*=i%!#;7$$"2%eQ3bF`n9!#;$"1%eQ3bF`n%!#;7$$"2M5LFUKCZ"!#;$"1K5LFUKCZ!#;7$$"2&*=]Q-psZ"!#;$"1%*=]Q-psZ!#;7$$"2L+W3FRC["!#;$"1L+W3FRC[!#;7$$"2z-iEE)f(["!#;$"1x-iEE)f([!#;7$$"1tF=k(GA\"!#:$"1Gx#=k(GA\!#;7$$"1nR:FRr(\"!#:$"1p'R:FRr(\!#;7$$"2/]nrl.B]"!#;$"1/]nrl.B]!#;7$$"2`n[>'=n2:!#;$"1`n[>'=n2&!#;7$$"2U(\O$H&z7:!#;$"1U(\O$H&z7&!#;7$$"2zZ[t!*pt^"!#;$"1yZ[t!*pt^!#;7$$"2'oo@RX^A:!#;$"1%oo@RX^A&!#;7$$"2ayWIF$pF:!#;$"1`yWIF$pF&!#;7$$"2)3[D$RZG`"!#;$"1(3[D$RZG`!#;7$$"2<"GYAfiP:!#;$"1<"GYAfiP&!#;7$$"2[[uE"QdU:!#;$"1[[uE"QdU&!#;7$$"2tU4y#4pZ:!#;$"1tU4y#4pZ&!#;7$$"2ZB"HK;z_:!#;$"1YB"HK;z_&!#;7$$"002QLQ!e:!#9$"/02QLQ!e&!#97$$"2#>!e8jfEc"!#;$"1">!e8jfEc!#;7$$"2G1\y6iyc"!#;$"1G1\y6iyc!#;7$$"1$[\i'f3t:!#:$"1G[\i'f3t&!#;7$$"2#e)Q@6?"y:!#;$"1#e)Q@6?"y&!#;7$$"2e?')))f"p#e"!#;$"1e?')))f"p#e!#;7$$"2sY#zQv7)e"!#;$"0nCzQv7)e!#:7$$"2<[EH\KFf"!#;$"19[EH\KFf!#;7$$"2%*y:$\"*3)f"!#;$"1%*y:$\"*3)f!#;7$$"2;#3(ypIGg"!#;$"19#3(ypIGg!#;7$$"2:rI"GH.3;!#;$"19rI"GH.3'!#;7$$"1=%e:o')Hh"!#:$"0=%e:o')Hh!#:7$$"2)ptd.a:=;!#;$"1)ptd.a:='!#;7$$"2l:"*Q!>!Hi"!#;$"1k:"*Q!>!Hi!#;7$$"2^\4dk@!G;!#;$"0&\4dk@!G'!#:7$$"1C:e='RLj"!#:$"0C:e='RLj!#:7$$"2hw*fH*ozj"!#;$"1hw*fH*ozj!#;7$$"1(eBBroHk"!#:$"1oeBBroHk!#;7$$"2_Q1r(R8[;!#;$"0&Q1r(R8['!#:7$$"2yb&)4=(=`;!#;$"1xb&)4=(=`'!#;7$$"2&f&pbTw!e;!#;$"1%f&pbTw!e'!#;7$$"2lT$)p20Nm"!#;$"1lT$)p20Nm!#;7$$"2wB82(HQo;!#;$"1uB82(HQo'!#;7$$"1"RNM;"ft;!#:$"14RNM;"ft'!#;7$$"2UIJ,c5$y;!#;$"1UIJ,c5$y'!#;7$$"2x&fF2,Z$o"!#;$"1x&fF2,Z$o!#;7$$"2^;Y!R[K)o"!#;$"1`;Y!R[K)o!#;7$$"2wStDV*R$p"!#;$"1wStDV*R$p!#;7$$"2c`(Hv2O)p"!#;$"1a`(Hv2O)p!#;7$$"2bQO8%[b.<!#;$"1bQO8%[b.(!#;7$$"2#*=hUMd&3<!#;$"1"*=hUMd&3(!#;7$$"2$3$Hg7tOr"!#;$"1$3$Hg7tOr!#;7$$"2[[TlaY(=<!#;$"1Z[TlaY(=(!#;7$$"2O5(3$\3Ms"!#;$"1O5(3$\3Ms!#;7$$"22yG*4;vG<!#;$"11yG*4;vG(!#;7$$"2btFtbINt"!#;$"1atFtbINt!#;7$$"20f5?"fiQ<!#;$"10f5?"fiQ(!#;7$$"24p%f;G]V<!#;$"14p%f;G]V(!#;7$$"2_^!Q#*z"*[<!#;$"1_^!Q#*z"*[(!#;7$$"28'[rOrg`<!#;$"18'[rOrg`(!#;7$$"2RIwuNH*e<!#;$"1PIwuNH*e(!#;7$$"21"*>R)*zPw"!#;$"1/"*>R)*zPw!#;7$$"23zUp!e3p<!#;$"13zUp!e3p(!#;7$$"2i6'*[$Qmt<!#;$"1i6'*[$Qmt(!#;7$$"1$*=Nuw()y<!#:$"0$*=Nuw()y(!#:7$$"2:Rpe)R"Ry"!#;$"18Rpe)R"Ry!#;7$$"2QT'G2q%*)y"!#;$"1NT'G2q%*)y!#;7$$"2ZpDJ^hRz"!#;$"1ZpDJ^hRz!#;7$$"2Lm)Q$))y()z"!#;$"1Lm)Q$))y()z!#;7$$"2NP@#)e')R!=!#;$"1MP@#)e')R!)!#;7$$"2dUL&3*\*3=!#;$"1dUL&3*\*3)!#;7$$"2.TY%pN<9=!#;$"1-TY%pN<9)!#;7$$"2t&QYSA!*==!#;$"1r&QYSA!*=)!#;7$$"1<d:2$GT#=!#:$"0<d:2$GT#)!#:7$$"2M&>PoR8H=!#;$"1M&>PoR8H)!#;7$$"1*oocWFT$=!#:$"1()oocWFT$)!#;7$$"1C"f?:V$R=!#:$"1R7f?:V$R)!#;7$$"1W303q9W=!#:$"0W303q9W)!#:7$$"2u()*o8o1\=!#;$"1s()*o8o1\)!#;7$$"2An'pj))\a=!#;$"0smpj))\a)!#:7$$"2cBR+9<%f=!#;$"1cBR+9<%f)!#;7$$"1=K%))*pWk=!#:$"0=K%))*pWk)!#:7$$"1=noNAcp=!#:$"1"=noNAcp)!#;7$$"2^bRP8kU(=!#;$"1^bRP8kU()!#;7$$"2i)\![?w#z=!#;$"1h)\![?w#z)!#;7$$"2smfO7]U)=!#;$"1smfO7]U))!#;7$$"28y_2nq&*)=!#;$"18y_2nq&*))!#;7$$"1Hq2BeE%*=!#:$"1)Gq2BeE%*)!#;7$$"2.Z*=aIo**=!#;$"1/Z*=aIo**)!#;7$$"2xp<worX!>!#;$"1xp<worX!*!#;7$$"2MVl[t3%4>!#;$"1MVl[t3%4*!#;7$$"2icsX65Y">!#;$"0mDd9,h9*!#:7$$"2nzK\`K)>>!#;$"1nzK\`K)>*!#;7$$"2iE">kTeC>!#;$"1iE">kTeC*!#;7$$"2#HrR$=I'H>!#;$"1#HrR$=I'H*!#;7$$"2Qxl\gaX$>!#;$"1Oxl\gaX$*!#;7$$"2M%z*)HF*)R>!#;$"1J%z*)HF*)R*!#;7$$"1)HA@p6X%>!#:$"0)HA@p6X%*!#:7$$"2)f-;Qn")\>!#;$"1)f-;Qn")\*!#;7$$"1>9LgP![&>!#:$"1)=9LgP![&*!#;7$$"2P)pI8Euf>!#;$"1P)pI8Euf*!#;7$$"2"*)p<&R&ok>!#;$"1*))p<&R&ok*!#;7$$"2_-5)>nsp>!#;$"1_-5)>nsp*!#;7$$"2zwl%R/2v>!#;$"1xwl%R/2v*!#;7$$"2E,:r5q*z>!#;$"1C,:r5q*z*!#;7$$"1*4K#3n![)>!#:$"1*)4K#3n![)*!#;7$$"2G"fAbp(**)>!#;$"1C"fAbp(**)*!#;7$$"2u$R/Zf8&*>!#;$"1x$R/Zf8&**!#;7$$"+'*******>!"*$"1&e;y&********!#;7dw7$$"+1+++?!"*$"1__YBcXCc!#C7$$"2Y.i4hd_+#!#;$"1`_.i4hd_!#=7$$"2$Rs#\AK)4?!#;$"0tRs#\AK)*!#<7$$"2<0vn&o(\,#!#;$"2<;0vn&o(\"!#=7$$"2PD#e!fb,-#!#;$"1p`Ae!fb,#!#<7$$"22mr2r4`-#!#;$"2V/mr2r4`#!#=7$$"2$\0'*R#)3I?!#;$"2o#\0'*R#)3I!#=7$$"1JC:Ih.N?!#:$"1tIC:Ih.N!#<7$$"2Z!pEXK:S?!#;$"0X!pEXK:S!#;7$$"2&4$G(\RDX?!#;$"2%[4$G(\RDX!#=7$$"1QJA^1]]?!#:$"1&y8B7l+0&!#<7$$"2Bib([>7b?!#;$"1:Acv[>7b!#<7$$"1ceANWKg?!#:$"1tbeANWKg!#<7$$"22Q0OG[b1#!#;$"1^!Q0OG[b'!#<7$$"1>YZHCeq?!#:$"1z=YZHCeq!#<7$$"22o.i"R:v?!#;$"1c!o.i"R:v!#<7$$"2%)>)3c)*e!3#!#;$"0$)>)3c)*e!)!#;7$$"1$z.-"[>&3#!#:$"1$Gz.-"[>&)!#<7$$"1u;dm9b!4#!#:$"1tt;dm9b!*!#<7$$"2-u2^,$H&4#!#;$"13Sx5:IH&*!#<7$$"1@oMX_\+@!#:$"2(4#oMX_\+"!#<7$$"2Fra()**[a5#!#;$"2`7Zv)**[a5!#<7$$"2$*)Hv?xh5@!#;$"2:*)Hv?xh5"!#<7$$"2.zZ5Ak`6#!#;$"2:!zZ5Ak`6!#<7$$"0lXG'R[?@!#9$"20]c%G'R[?"!#<7$$"12kpN>!e7#!#:$"282kpN>!e7!#<7$$"2<8'pY7VI@!#;$"1<8'pY7VI"!#;7$$"1`**RH5VN@!#:$"20`**RH5VN"!#<7$$"214iTH'fS@!#;$"2o!4iTH'fS"!#<7$$"2.0@!)\\c9#!#;$"2E]5-)\\c9!#<7$$"1&\&eK(Q0:#!#:$"2$[\&eK(Q0:!#<7$$"2wjxRRnf:#!#;$"2lPw(RRnf:!#<7$$"1Zzo(GX3;#!#:$"2(o%zo(GX3;!#<7$$"2xE*Q![`g;#!#;$"2ln#*Q![`g;!#<7$$"2NImq(Gxq@!#;$"2M.j1xGxq"!#<7$$"2%=.>CC$f<#!#;$"2N=.>CC$f<!#<7$$"126%f:(y!=#!#:$"2A26%f:(y!=!#<7$$"270[%\<'e=#!#;$"2B^![%\<'e=!#<7$$"1MB:#4B3>#!#:$"0MB:#4B3>!#:7$$"2tSq"er,'>#!#;$"2F2/<er,'>!#<7$$"28?v5m>5?#!#;$"23,_2h'>5?!#<7$$"2s&G#GWNh?#!#;$"21dG#GWNh?!#<7$$"2)RZJj)37@#!#;$"2aRZJj)37@!#<7$$"28rT)43(e@#!#;$"16rT)43(e@!#;7$$"1;?mER@@A!#:$"2<;?mER@@#!#<7$$"2Y&=/uG*fA#!#;$"2`a=/uG*fA!#<7$$"1GVqG#)3JA!#:$"20GVqG#)3J#!#<7$$"1@*oK8lfB#!#:$"2x?*oK8lfB!#<7$$"1&3L!4.QTA!#:$"2s%3L!4.QT#!#<7$$"1u'[LXpgC#!#:$"1Qn[LXpgC!#;7$$"1G))3u;R^A!#:$"1y#))3u;R^#!#;7$$"1KI^+BCcA!#:$"0KI^+BCc#!#:7$$"1*o9N7[:E#!#:$"2())o9N7[:E!#<7$$"2Cq\9:EhE#!#;$"1Cq\9:EhE!#;7$$"1CY)3**R8F#!#:$"1Ri%)3**R8F!#;7$$"2n(>Q-jPwA!#;$"1n(>Q-jPw#!#;7$$"1n)yPK49G#!#:$"1n')yPK49G!#;7$$"04)fHQU'G#!#9$"2w*3)fHQU'G!#<7$$"1*yT)*>T7H#!#:$"2.*yT)*>T7H!#<7$$"2(oOl/*[kH#!#;$"1'oOl/*[kH!#;7$$"2t'e%\A79I#!#;$"21ne%\A79I!#<7$$"1dz$e)ej1B!#:$"2:dz$e)ej1$!#<7$$"2'*[Oobk8J#!#;$"2c*[Oobk8J!#<7$$"2aW2Ni!f;B!#;$"2;Xu]B1f;$!#<7$$"1fOq%G'f@B!#:$"2veOq%G'f@$!#<7$$"2.U!)>w*eEB!#;$"1-U!)>w*eE$!#;7$$"2F**\$oa!=L#!#;$"1E**\$oa!=L!#;7$$"1(\AVK4mL#!#:$"0(\AVK4mL!#:7$$"2:&=%*H"H:M#!#;$"18&=%*H"H:M!#;7$$"1=p#*z6'pM#!#:$"0=p#*z6'pM!#:7$$"2%3)\iXz=N#!#;$"1#3)\iXz=N!#;7$$"1rO.:$4pN#!#:$"22rO.:$4pN!#<7$$"20rc=bC?O#!#;$"2B5n&=bC?O!#<7$$"0u!*)\ksmB!#9$"20S2*)\ksm$!#<7$$"1Bh$4_Q<P#!#:$"2kAh$4_Q<P!#<7$$"134xRCrwB!#:$"2'z!4xRCrw$!#<7$$"0uUo)H.#Q#!#9$"2&*RF%o)H.#Q!#<7$$"12#["R"GnQ#!#:$"1p?["R"GnQ!#;7$$"1z*Q-PX@R#!#:$"0z*Q-PX@R!#:7$$"2DlZO+MqR#!#;$"1BlZO+MqR!#;7$$"0/w30r=S#!#9$"29Sg(30r=S!#<7$$"1nBcIC22C!#:$"2'oOi0VsqS!#<7$$"13<!4&[H7C!#:$"1zq,4&[H7%!#;7$$"1r69![YqT#!#:$"2uq69![YqT!#<7$$"0&oK*\#4AC!#9$"1(\oK*\#4A%!#;7$$"1(zv3#p,FC!#:$"2&ozv3#p,F%!#<7$$"19myX]NKC!#:$"1Ph'yX]NK%!#;7$$"1$\#*z+upV#!#:$"0$\#*z+upV!#:7$$"2XB4S0zAW#!#;$"1WB4S0zAW!#;7$$"2aWgh2msW#!#;$"1`Wgh2msW!#;7$$"2ZD;"H\?_C!#;$"2lai6H\?_%!#<7$$"2))[m4rZrX#!#;$"1')[m4rZrX!#;7$$"0Ozb.*=iC!#9$"2')f$zb.*=i%!#<7$$"2us8_vKvY#!#;$"2MFP@bF`n%!#<7$$"2OPVGUKCZ#!#;$"1MPVGUKCZ!#;7$$"2L6TR-psZ#!#;$"2/86%R-psZ!#<7$$"2kC94FRC[#!#;$"1jC94FRC[!#;7$$"1N;ri#)f([#!#:$"1Zj6FE)f([!#;7$$"1eQ@k(GA\#!#:$"2kdQ@k(GA\!#<7$$"276jr#Rr(\#!#;$"06J;FRr(\!#:7$$"2bGerl.B]#!#;$"1aGerl.B]!#;7$$"1))z">'=n2D!#:$"1w)z">'=n2&!#;7$$"2Mz8LH&z7D!#;$"1Lz8LH&z7&!#;7$$"1)**ys!*pt^#!#:$"0)**ys!*pt^!#:7$$"20"o7RX^AD!#;$"1."o7RX^A&!#;7$$"2D,MHF$pFD!#;$"1C,MHF$pF&!#;7$$"2%>M7$RZG`#!#;$"1%>M7$RZG`!#;7$$"13BJAfiPD!#:$"1"3BJAfiP&!#;7$$"2(*=/D"QdUD!#;$"1(*=/D"QdU&!#;7$$"1k'=w#4pZD!#:$"1Qm=w#4pZ&!#;7$$"2$o+3K;z_D!#;$"1$o+3K;z_&!#;7$$"1(*[dL$Q!eD!#:$"1o*[dL$Q!e&!#;7$$"1"Q26jfEc#!#:$"17Q26jfEc!#;7$$"19wd<@'yc#!#:$"1Uhxv6iyc!#;7$$"2&Rr&f'f3tD!#;$"1#Rr&f'f3t&!#;7$$"2xPE=6?"yD!#;$"1wPE=6?"y&!#;7$$"2&Rab)f"p#e#!#;$"1'Rab)f"p#e!#;7$$"1d*R%Qv7)e#!#:$"1s&*R%Qv7)e!#;7$$"2<bbD\KFf#!#;$"1;bbD\KFf!#;7$$"2EVB*["*3)f#!#;$"1FVB*["*3)f!#;7$$"1*\fupIGg#!#:$"0*\fupIGg!#:7$$"0e)pFH.3E!#9$"1'z&)pFH.3'!#;7$$"2:Z16o')Hh#!#;$"1:Z16o')Hh!#;7$$"2&[Z5.a:=E!#;$"1([Z5.a:='!#;7$$"1\&*R.>!Hi#!#:$"1#\&*R.>!Hi!#;7$$"2)3u>X;-GE!#;$"1)3u>X;-G'!#;7$$"1m"[!='RLj#!#:$"1f;[!='RLj!#;7$$"20*y/H*ozj#!#;$"1/*y/H*ozj!#;7$$"17<v6(oHk#!#:$"1=r^<roHk!#;7$$"2%\Q^wR8[E!#;$"1%\Q^wR8['!#;7$$"14GP!=(=`E!#:$"04GP!=(=`'!#:7$$"2QDP\Tw!eE!#;$"1ODP\Tw!e'!#;7$$"2kRHj20Nm#!#;$"1kRHj20Nm!#;7$$"2dqR+(HQoE!#;$"1cqR+(HQo'!#;7$$"2l-TF;"ftE!#;$"1m-TF;"ft'!#;7$$"2B1=%f0JyE!#;$"1C1=%f0Jy'!#;7$$"1x?a1,Z$o#!#:$"1t2Ul5qMo!#;7$$"1mGHQ[K)o#!#:$"0mGHQ[K)o!#:7$$"0")*zJ%*R$p#!#9$"1(4)*zJ%*R$p!#;7$$"1$4/Xxg$)p#!#:$"0$4/Xxg$)p!#:7$$"1m@_S[b.F!#:$"0m@_S[b.(!#:7$$"0'pUVtb3F!#9$"1*fpUVtb3(!#;7$$"1;Y<DJn8F!#:$"0;Y<DJn8(!#:7$$"1*\mcaY(=F!#:$"1*)\mcaY(=(!#;7$$"0Z$>#\3Ms#!#9$"1)pM>#\3Ms!#;7$$"2Wx8!4;vGF!#;$"1Ux8!4;vG(!#;7$$"2Mh$Rc0`LF!#;$"1Nh$Rc0`L(!#;7$$"1(3c5"fiQF!#:$"0(3c5"fiQ(!#:7$$"2)z1i:G]VF!#;$"1%z1i:G]V(!#;7$$"1V[Q"*z"*[F!#:$"1K%[Q"*z"*[(!#;7$$"1L/qNrg`F!#:$"1EV+d82Ov!#;7$$"2meSkNH*eF!#;$"1ieSkNH*e(!#;7$$"1"zkG)*zPw#!#:$"0"zkG)*zPw!#:7$$"1[k'e!e3pF!#:$"1wWme!e3p(!#;7$$"1h9!Q$QmtF!#:$"14Y,Q$Qmt(!#;7$$"2FQOKnx)yF!#;$"1CQOKnx)y(!#;7$$"2btLZ)R"Ry#!#;$"1dtLZ)R"Ry!#;7$$"1E181q%*)y#!#:$"0E181q%*)y!#:7$$"2([)\>^hRz#!#;$"1([)\>^hRz!#;7$$"1[N>#))y()z#!#:$"0[N>#))y()z!#:7$$"2vU0qe')R!G!#;$"1sU0qe')R!)!#;7$$"2li(H2*\*3G!#;$"1ki(H2*\*3)!#;7$$"1;(*=oN<9G!#:$"1ir*=oN<9)!#;7$$"2$[#)=RA!*=G!#;$"1zC)=RA!*=)!#;7$$"1/#feIGT#G!#:$"1U?feIGT#)!#;7$$"2wTbq'R8HG!#;$"1vTbq'R8H)!#;7$$"1z@LWu7MG!#:$"1$z@LWu7M)!#;7$$"2:v,2:V$RG!#;$"1<v,2:V$R)!#;7$$"2iDum+ZT%G!#;$"1iDum+ZT%)!#;7$$"2.h$H7o1\G!#;$"1.h$H7o1\)!#;7$$"1x'yA'))\aG!#:$"0x'yA'))\a)!#:7$$"1n:gQrTfG!#:$"0n:gQrTf)!#:7$$"0V&Q(*pWkG!#9$"1,V&Q(*pWk)!#;7$$"2#p%3UBi&pG!#;$"0p%3UBi&p)!#:7$$"1*\UA8kU(G!#:$"1"*\UA8kU()!#;7$$"2;)yG.iFzG!#;$"19)yG.iFz)!#;7$$"1nE7A,D%)G!#:$"1mmA@7]U))!#;7$$"1*\%>p1d*)G!#:$"1*)\%>p1d*))!#;7$$"2d'**\@eE%*G!#;$"1d'**\@eE%*)!#;7$$"1Q2f_Io**G!#:$"0Q2f_Io**)!#:7$$"16%**forX!H!#:$"11T**forX!*!#;7$$"2&)zFKt3%4H!#;$"1%)zFKt3%4*!#;7$$"2e79H65Y"H!#;$"1f79H65Y"*!#;7$$"2nY`K`K)>H!#;$"1lY`K`K)>*!#;7$$"2'HH\iTeCH!#;$"1&HH\iTeC*!#;7$$"2'3'y;=I'HH!#;$"1)3'y;=I'H*!#;7$$"1cvA.YbMH!#:$"1ebFKgaX$*!#;7$$"2FPQ"GF*)RH!#;$"1FPQ"GF*)R*!#;7$$"29DW.p6X%H!#;$"19DW.p6X%*!#;7$$"1$*4OOn")\H!#:$"1G*4OOn")\*!#;7$$"2U?7&eP![&H!#;$"0/A^eP![&*!#:7$$"2M,o9hU(fH!#;$"1L,o9hU(f*!#;7$$"2vC=LR&okH!#;$"1vC=LR&ok*!#;7$$"2'=6$zrE(pH!#;$"1%=6$zrE(p*!#;7$$"2m[lvVq](H!#;$"1m[lvVq](*!#;7$$"2C8&>0,(*zH!#;$"1C8&>0,(*z*!#;7$$"1sGH1n![)H!#:$"0sGH1n![)*!#:7$$"10gE`p(**)H!#:$"1_+mK&p(**)*!#;7$$"2ORj]%f8&*H!#;$"1MRj]%f8&**!#;7$$"+%*******H!"*$"1[avV********!#;-%&COLORG6&%$RGBG$")C)eq%!")$""!!""$"('>!\&!")-%'POINTSG6)7$$!#I!""$""&!""7$$!#?!""$""&!""7$$!#5!""$""&!""7$$""!!""$""&!""7$$"#5!""$""&!""7$$"#?!""$""&!""7$$"#I!""$""&!""-%%VIEWG6$;$!#I!""$"#I!""%(DEFAULTG-&%&_AXISG6#"""6'-%+_GRIDLINESG6&-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#""!-%*THICKNESSG6#""!-%-TRANSPARENCYG6#$""!!""-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#""!-%*THICKNESSG6#""!-%-TRANSPARENCYG6#$""!!""-&%&_AXISG6#""#6'-%+_GRIDLINESG6&-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#""!-%*THICKNESSG6#""!-%-TRANSPARENCYG6#$""!!""-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#""!-%*THICKNESSG6#""!-%-TRANSPARENCYG6#$""!!""-%+AXESLABELSG6$-I#miG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"65Q"x6"/%'familyGQ!6"/%%sizeGQ#106"/%%boldGQ&false6"/%'italicGQ%true6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ([0,0,0]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%,mathvariantGQ'italic6"Q!6"-%%ROOTG6'-%)BOUNDS_XG6#$"$I"!""-%)BOUNDS_YG6#$"$?"!""-%-BOUNDS_WIDTHG6#$"%qP!""-%.BOUNDS_HEIGHTG6#$"%gM!""-%)CHILDRENG6"

The formal sum converges to the periodic extension of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInhGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ==, except at the jump discontinuities, where it converges to the midpoint of the jump. This is the correct limit of a Fourier series.

The exponential form of the series:

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LCYjIiIiIiIjRiQtSSRTdW1HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JCwmKioqJkYjRiReI0YkRiRGJEkjUGlHRikhIiJJImlHRitGMi1JJGV4cEdGKDYjKioqJkYlRiRGMEYkRiRGMUYkRjNGJEkieEdGK0YkRiRGJCoqLCRGL0YkRiRGMUYyRjNGMi1GNTYjLCQqKiwkRjhGJEYkRjFGJEYzRiRGOUYkRjJGJEYyL0YzO0YkSSlpbmZpbml0eUdGKUYk

The Hartley form of the series:

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LCYjIiIiIiIjRiQtSSRTdW1HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JCwmKipGI0YkSSNQaUdGKSEiIkkiaUdGK0YwLCYtSSRjb3NHRig2IywkKipGJUYkRi9GJEYxRiRJInhHRitGJEYkRiQtSSRzaW5HRihGNUYkRiRGMCoqRiNGJEYvRjBGMUYwLCZGM0YkRjlGMEYkRiQvRjE7RiRJKWluZmluaXR5R0YpRiQ=

<Text-field style="Heading 2" layout="Heading 2">Example 2</Text-field>

JSFH

Use the FourierSeries command to obtain a sine series for 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.

JSFH

No general representation for the coefficients can be found, so Maple returns the unevaluated integrals that determine these coefficients.

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LUkkU3VtRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQsJCooIiIjIiIiLUkkaW50R0YkNiQqJi1JJGV4cEdGJDYjKiQpSSJ4R0YnIiIkRixGLC1JJHNpbkdGJDYjKihJI1BpR0YlRixJImlHRidGLEY2RixGLC9GNjsiIiFGLEYsRjhGLEYsL0Y9O0YsSSlpbmZpbml0eUdGJQ==

JSFH

The coefficient integrals can be evaluated numerically with the following syntax. Note that the number of terms must be finite.

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LCgqJiQiJ3ckZSIhIiYiIiItSSRzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IywkKiYkIidmVEpGJkYnSSJ4R0YtRidGJ0YnRicqJiQiJ29GTyEiJ0YnLUYpNiMsJComJCInPSRHJ0YmRidGM0YnRidGJyEiIiomJCInJz49KEY3RictRik2IywkKiYkIid4QyUqRiZGJ0YzRidGJ0YnRic=

JSFH

To change the number of digits from the default (6) to, say, 10, use the evalfIntoptions parameter.

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LCYqJiQiK2dKdyRlIiEiKiIiIi1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCQqJiQiK2FFZlRKRiZGJ0kieEdGLUYnRidGJ0YnKiYkIisnNHJ3aSQhIzVGJy1GKTYjLCQqJiQiKzNgPSRHJ0YmRidGM0YnRidGJyEiIg==

JSFH

<Text-field style="Heading 2" layout="Heading 2">Example 3</Text-field>

JSFH

Obtain a sine series for 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, by means of the FourierSeries command.

By default, integrals include the option "AllSolutions" so that all the coefficients are obtained from just the integration.

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

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

JSFH

Thus, the FourierSeries command avoids the trap that catches the student who simply evaluates

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LCQqKiIiIyIiIiwmRiUhIiIpRidJImtHNiJGJUYlRilGJywmKiQpRilGJEYlRiUiIiVGJ0YnRiU=

JSFH

at 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and gets a division-by-zero error at LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjJGJ0Y5Rjk=. In a partial sum, this subtlety can go unnoticed:

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LCgqKCMiIikiIiQiIiJJI1BpRyUqcHJvdGVjdGVkRyEiIi1JJHNpbkc2JEYpSShfc3lzbGliRzYiNiNJInhHRi9GJ0YnKigjRiUiIzpGJ0YoRiotRiw2IywkKiZGJkYnRjFGJ0YnRidGKiooI0YlIiQwIkYnRihGKi1GLDYjLCQqJiIiJkYnRjFGJ0YnRidGKg==

JSFH

<Text-field style="Heading 2" layout="Heading 2">Example 4</Text-field>

JSFH

Apply the FourierSeries command to the function 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.

JSFH

Obtain a sine series with a fixed number of terms:

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LCoqKiIjayIiIilJI1BpRyUqcHJvdGVjdGVkRyIiIyEiIi1JJHNpbkc2JEYoSShfc3lzbGliRzYiNiNJInhHRi9GJS1GLDYjSSJ5R0YvRiVGJSoqI0YkIiNGRiVGJkYqRitGJS1GLDYjLCQqJiIiJEYlRjRGJUYlRiVGJSoqRjZGJUYmRiotRiw2IywkKiZGPEYlRjFGJUYlRiVGMkYlRiUqKiNGJCIkSChGJUYmRipGPkYlRjhGJUYl

JSFH

In this instance, a general expression for the coefficients can be inferred from the following inert representation.

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LUkkU3VtRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQtRiM2JCwkKjAiIzsiIiIsJikhIiImSSJrR0YnNiNGLkYuRi5GMUYuKUYyIiIkRjEsJilGMSZGMzYjIiIjRi5GLkYxRi4pRjlGNkYxKUkjUGlHRiVGO0YxLUkoUHJvZHVjdEdGJDYkLUkkc2luR0YkNiMqKiZGMzYjSSJpR0YnRi5GPkYuLCYmNyRJInhHRidJInlHRidGR0YuJjckIiIhRlBGR0YxRi4mNyRGPkY+RkdGMS9GSDtGLkY7Ri5GLi9GOTtGLkkibUdGJy9GMjtGLkkibkdGJw==

JSFH

The product symbol represents terms of the form LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEkc2luRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUklbXN1YkdGJDYlLUYsNiVRImtGJy9GMFEldHJ1ZUYnL0YzUSdpdGFsaWNGJy1GIzYmLUkjbW5HRiQ2JFEiMUYnRjItSSNtb0dGJDYtUSJ+RidGMi8lJmZlbmNlR0YxLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRjEvJSpzeW1tZXRyaWNHRjEvJShsYXJnZW9wR0YxLyUubW92YWJsZWxpbWl0c0dGMS8lJ2FjY2VudEdGMS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRmhuRkBGQi8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUYsNiVRInhGJ0ZARkJGMkYyRistRjY2JC1GIzYmLUY7NiVGPS1GIzYlLUZHNiRRIjJGJ0YyRkBGQkZbb0ZKLUYsNiVRInlGJ0ZARkJGMkYyRjI=. When LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRImlGJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvRjZRJ25vcm1hbEYn is even, the sine factor is zero, so only terms with odd LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRImlGJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvRjZRJ25vcm1hbEYn are nonzero. That implies the coefficients are 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 for LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRImlGJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvRjZRJ25vcm1hbEYn odd.

JSFH

<Text-field style="Heading 1" layout="Heading 1">Bessel Series</Text-field>

<Text-field style="Heading 2" layout="Heading 2">The <Font family="Arial">BesselSeries</Font> Command</Text-field>

JSFH

For LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInhGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ== on LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbW5HRiQ2JFEiMEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RJiZsZXE7RidGLy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOC8lKXN0cmV0Y2h5R0Y4LyUqc3ltbWV0cmljR0Y4LyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZHLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJ0YyLUZLNiVRImNGJ0ZORlFGLw==, a formal Bessel expansion in terms of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiSkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMEYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdGPS1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYvNiVRInhGJ0YyRjVGPkY+Rj4= is obtained with

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LUkkU3VtRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQsJCosIiIjIiIiLUkkaW50R0YkNiQqKC1JImZHRic2I0kieEdGJ0YsRjRGLC1JKEJlc3NlbEpHRiQ2JCIiISooLUktQmVzc2VsSlplcm9zR0YkNiRGOEkiaUdGJ0YsRjRGLEkiY0dGJyEiIkYsL0Y0O0Y4Rj5GLClGPkYrRj8pLUY2NiRGLEY6RitGP0Y1RixGLC9GPTtGLEkibkdGJw==

By switching to the extended typesetting mode with

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

Maple will display the requisite Bessel functions with the more standard notation 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. Thus, the formal expansion

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 becomes

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSRTdW1HRiU2JCwkKiwiIiMiIiItSSRpbnRHRiU2JCooLUkiZkdGKDYjSSJ4R0YoRjJGOkYyLUkoQmVzc2VsSkdGJTYkIiIhKigtSS1CZXNzZWxKWmVyb3NHRiU2JEY+SSJpR0YoRjJGOkYySSJjR0YoISIiRjIvRjo7Rj5GREYyKUZERjFGRSktRjw2JEYyRkBGMUZFRjtGMkYyL0ZDO0YySSJuR0YoRis=

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

To simplify the display of the zeros of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiSkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMEYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdGPUY+, execute the following alias command.

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

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

The formal expansion

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 now becomes

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyMtSSRTdW1HRiU2JCwkKiwiIiMiIiItSSRpbnRHRiU2JCooLUkiZkdGKDYjSSJ4R0YoRjJGOkYyLUkoQmVzc2VsSkdGJTYkIiIhKigtSSdsYW1iZGFHRig2JEY+SSJpR0YoRjJGOkYySSJjR0YoISIiRjIvRjo7Rj5GREYyKUZERjFGRSktRjw2JEYyRkBGMUZFRjtGMkYyL0ZDO0YySSJuR0YoRis=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

If, for example, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInhGJ0YvRjIvRjNRJ25vcm1hbEYnRj0tSSNtb0dGJDYtUSI9RidGPS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRS8lKXN0cmV0Y2h5R0ZFLyUqc3ltbWV0cmljR0ZFLyUobGFyZ2VvcEdGRS8lLm1vdmFibGVsaW1pdHNHRkUvJSdhY2NlbnRHRkUvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZURjpGPQ== and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1JI21uR0YkNiRRIjFGJ0Y5Rjk=, the following partial sum of the Bessel series expansion can be obtained.

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LCgqKiktSSdsYW1iZGFHNiI2JCIiISIiIiIiIyEiIiwmKihGK0YqRiVGKi1JKEJlc3NlbEpHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRic2JEYqRiVGKkYsKihJI1BpR0YyRipGL0YqLUkoU3RydXZlSEdGMTYkRilGJUYqRipGKilGL0YrRiwtRjA2JEYpKiZGJUYqSSJ4R0YnRipGKkYsKiopLUYmNiRGKUYrRitGLCwmKihGK0YqRkFGKi1GMDYkRipGQUYqRioqKEY2RipGRUYqLUY4NiRGKUZBRipGLEYqKUZFRitGLC1GMDYkRikqJkZBRipGPkYqRipGKioqKS1GJjYkRikiIiRGK0YsLCYqKEYrRipGUEYqLUYwNiRGKkZQRipGKiooRjZGKkZVRiotRjg2JEYpRlBGKkYsRiopRlVGK0YsLUYwNiRGKSomRlBGKkY+RipGKkYq

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

Interestingly enough, Maple is able to evaluate the integrals

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

in terms of the StruveH functions 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. Use of the numeric option leads to

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LCgqJiQiJ1x1IikhIiciIiItSShCZXNzZWxKRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQiIiEsJComJCInJFtTIyEiJkYnSSJ4R0YtRidGJ0YnRicqJiQiJ1tMNkY0RictRik2JEYvLCQqJiQiJzM/YkY0RidGNUYnRidGJyEiIiomJCInIUgpekYmRictRik2JEYvLCQqJiQiJ3RgJylGNEYnRjVGJ0YnRidGJw==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

suggesting the graph in Figure 1.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

-%%PLOTG6(-%'CURVESG6$7d^l7$$""!!""$!'N89!"'7$$"-D"G1?d'!#:$!2xnDW*\f79!#<7$$"-Dc7S98!#9$!2W+7_!4L59!#<7$$".vV)=gr>!#:$!1<(fN^glS"!#;7$$",D^-)GE!#8$!1Q=Q]%)G,9!#;7$$"-voP?VR!#9$!2E]r#RqE'Q"!#<7$$"+D]gd_!#7$!+#RS`O"!#57$$"+N?"\a(!#7$!2sql^Jl^J"!#<7$$"+X!>A$)*!#7$!+%4w"[7!#57$$"+&4&o(\"!#6$!+=JbT5!#57$$"+#[eb,#!#6$!*E%R&o(!#57$$"+20(4`#!#6$!*&fi>X!#57$$"+KM#)3I!#6$!*V#>#Q"!#57$$"+dCh.N!#6$"+J<im=!#67$$"+vRK:S!#6$"*h.r,&!#57$$"+FWRDX!#6$"+s2Ebx!#67$$"+$ek+0&!#6$"+R0B&***!#67$$"+UV>7b!#6$"+O92S6!#57$$",&o'=Bx&!#7$"2[ek(HSX%>"!#<7$$"+&*HWKg!#6$"+GO,J7!#57$$"+1#RI;'!#6$"2*4%\J?$yU7!#<7$$"+<aj$H'!#6$"2N&4TdEF]7!#<7$$"+G;BCk!#6$"2()zhQk.OD"!#<7$$"+Ry#[b'!#6$"+l1#HD"!#57$$",b8Nl!o!#7$"1"Rb@H74C"!#;7$$"+KCCeq!#6$"+1s-;7!#57$$"+rn"oG(!#6$"2))=7HJ^O="!#<7$$"*6"R:v!#5$"*D#RV6!"*7$$"+0^)*e!)!#6$"+HK*[-"!#57$$"+A0[>&)!#6$"+d*fG7*!#67$$"+mh9b!*!#6$"+95=ey!#67$$"+D5IH&*!#6$"+^gBFp!#67$$",v`7%*y*!#7$"1VT%)H@vNl!#<7$$"+0C&\+"!#5$"21++SRr%[i!#=7$$"-v)yOt,"!#7$"1E;pzO)=:'!#<7$$",D<@(H5!#6$"2C!4GuHp#3'!#=7$$"-Dcb5U5!#7$"1c%GAib</'!#<7$$"*%**[a5!"*$"21++IB_(Hg!#=7$$"2,+]_u6u1"!#<$"1h$H'oWh[g!#<7$$",0bL.3"!#6$"0M%pDb))*4'!#;7$$"-vb`D$4"!#7$"1-t-'G;P='!#<7$$"+hr<16!#5$"+#=Y+I'!#67$$"2*****\i'4*H6!#<$"1G6!p=<tf'!#<7$$"+k@k`6!#5$"+"e9(**p!#67$$"+$eR[?"!#5$"+j:D'>)!#67$$"+7$>!e7!#5$"+)Qk<$)*!#67$$"+BCJ/8!#5$"+w&fw9"!#57$$"*D5VN"!"*$"+=ksN8!#57$$"+)*G'fS"!#5$"+3l0F:!#57$$"+Q\\c9!#5$"+s(*f(p"!#57$$"+%G(Q0:!#5$"+O+/O=!#57$$"+)*Qnf:!#5$"+)3b)\>!#57$$"2)*****pOjSe"!#<$"1j%Q9#ot&)>!#;7$$"+OGX3;!#5$"+MC'=,#!#57$$")Q\M;!")$"2)4+&=x!4H?!#<7$$"+kZ`g;!#5$"+)>*oN?!#57$$",vuJTo"!#6$"2w;C$3;/L?!#<7$$"+J(Gxq"!#5$"+l5*G-#!#57$$"+nk_L<!#5$"1'y'*)3**>/?!#;7$$"+.UKf<!#5$"+%GB)y>!#57$$"+@:(y!=!#5$"*<$3=>!"*7$$"+duhe=!#5$"+eQIY=!#57$$"+%)3B3>!#5$"+`2))z<!#57$$"+X:<g>!#5$"+e#pls"!#57$$"*1%=&)>!"*$"2Ag-[&)e+r"!#<7$$"+vl>5?!#5$"*i))3q"!"*7$$"+%[vd.#!#5$"2RLpzB:**p"!#<7$$"+$Ra81#!#5$"+sT/3<!#57$$"2-++b\@n3#!#<$"2V:'*Qxdas"!#<7$$"+)f)37@!#5$"+Q:I_<!#57$$"+k!3(e@!#5$"+M0kD=!#57$$"+L#R@@#!#5$"*%oRW>!"*7$$"+2(G*fA!#5$"+1_pv?!#57$$"+bA)3J#!#5$"+C(RDB#!#57$$"+,8lfB!#5$"+K#R))Q#!#57$$"+fI!QT#!#5$"+wz(ob#!#57$$"+.XpgC!#5$"*7()yo#!"*7$$"+6n"R^#!#5$"+QKw5G!#57$$"+wHUiD!#5$")w#G*G!")7$$"2(*****44_*)e#!#<$"2`(3%G*QXCH!#<7$$"+17[:E!#5$"+#)G`YH!#57$$"+Y8PQE!#5$"17y0>y/eH!#;7$$"+'[h7m#!#5$"+s&oG'H!#57$$",NoIto#!#6$"1;y;^=ugH!#;7$$"+"))*R8F!#5$"*>%H^H!"*7$$"2'******Q9eQF!#<$"1h7Gs\;OH!#;7$$"+(*HwjF!#5$"+`h?;H!#57$$"+6K49G!#5$"+&o?m'G!#57$$"*FQU'G!"*$"+LW$H"G!#57$$"+t>T7H!#5$"+%=Wqw#!#57$$",v\]%QH!#6$"0c?h<2xu#!#:7$$"+A!*[kH!#5$"+V()zLF!#57$$"+CcI*)H!#5$"28gRb3qls#!#<7$$"+EA79I!#5$"+A]+EF!#57$$",0`S-/$!#6$"2cSqHYjKt#!#<7$$"+N)ej1$!#5$"+Yk/\F!#57$$"2(****\!>-+4$!#<$"2Mbclz&*3x#!#<7$$"+Ybk8J!#5$"+G"\**z#!#57$$"+8i!f;$!#5$"+HXv))G!#57$$"+EG'f@$!#5$"+3y,-I!#57$$"+*f(*eE$!#5$"+_q&f8$!#57$$"+jY0=L!#5$"+Wo(*)G$!#57$$"+CK4mL!#5$"+UKTKM!#57$$"*G"H:M!"*$"+_9MsN!#57$$"+"y6'pM!#5$"+JTG3P!#57$$"+XXz=N!#5$"+#3()o!Q!#57$$"+LJ4pN!#5$"+^0eyQ!#57$$",vJpYf$!#6$"2.,rJ4nH!R!#<7$$"+-bC?O!#5$"+1C@>R!#57$$",D*\vVO!#6$"1$))fz,&=FR!#;7$$"+$[ksm$!#5$"+@]&)GR!#57$$",&Q[K#p$!#6$"1j%*>$>cU#R!#;7$$"+%>&Q<P!#5$"+K@#Q"R!#57$$"+$QCrw$!#5$"+GR^zQ!#57$$"+a)H.#Q!#5$"+-c&4$Q!#57$$"+y8GnQ!#5$"+%yGpy$!#57$$"+*o`9#R!#5$"+J$pcu$!#57$$"2(****\co*e%R!#<$"2E]-3^%GLP!#<7$$"+C+MqR!#5$"+U'fgs$!#57$$",0EDX*R!#6$"1*p#Q2StCP!#;7$$"+(\5(=S!#5$"+^1!)HP!#57$$",bR<Z/%!#6$"1u]C"z*)Gu$!#;7$$"+%HC22%!#5$"+MNBkP!#57$$"+'ROo4%!#5$"1rZ*)pJ4%z$!#;7$$"+)\[H7%!#5$"+/THKQ!#57$$"+"zk/<%!#5$"+#*>(>#R!#57$$"+%)\#4A%!#5$"+(*HyTS!#57$$")#p,F%!")$"+h)ok<%!#57$$"*X]NK%!"*$"+x)oDL%!#57$$"+s+upV!#5$"+2ELnW!#57$$"+L0zAW!#5$"+9+[6Y!#57$$"2(*****\vgEZ%!#<$"+Eq%ys%!#57$$"+&G\?_%!#5$"+$*R3=[!#57$$",X>jna%!#6$"2%>'y]c9D&[!#<7$$"+/rZrX!#5$"*b,%z[!"*7$$",vs$o'f%!#6$"1&p6*f)))*)*[!#;7$$"+^.*=i%!#5$"+0dz5\!#57$$",&\*3'[Y!#6$"1EU-1&)=:\!#;7$$"+[vKvY!#5$"+#>U="\!#57$$",l)e#)*p%!#6$"2NJ9Jh'p-\!#<7$$"+DUKCZ!#5$"+UDc))[!#57$$"+P-psZ!#5$"+y!4(\[!#57$$"+2FRC[!#5$"+TZ)**z%!#57$$"+DE)f([!#5$"+**f]_Z!#57$$"+TwGA\!#5$"+D)[/s%!#57$$"+cMr\\!#5$"1R\#)f884Z!#;7$$"+r#Rr(\!#5$"+'fC]q%!#57$$",:#z3+]!#6$"1kluIu%yq%!#;7$$"+sl.B]!#5$"2.++S&4&or%!#<7$$"1,++&fx)\]!#;$"1pr?N`jNZ!#;7$$"+='=n2&!#5$"+c(fNw%!#57$$"+NH&z7&!#5$"+hP,U[!#57$$"+v!*pt^!#5$"+zN$z$\!#57$$"+#RX^A&!#5$"+DRqp]!#57$$"1*****RtKpF&!#;$"+(3"o>_!#57$$"+NRZG`!#5$"+Go(eP&!#57$$"+E#fiP&!#5$"+$per^&!#57$$"+J"QdU&!#5$"+ZxV]c!#57$$"+"G4pZ&!#5$"+4:eld!#57$$"+Ej"z_&!#5$"+'zx0&e!#57$$"+M)\Tb&!#5$"1'R_-$QK")e!#;7$$"1*****>M$Q!e&!#;$"+a,'H!f!#57$$"1******G)*[.c!#;$"1[I#49IX"f!#;7$$"+;jfEc!#5$"+#H3$>f!#57$$"+^(3El&!#5$"1iTB#G>q"f!#;7$$"+'=@'yc!#5$"+_rJ2f!#57$$"+F/u/d!#5$"1d2"=Qf5*e!#;7$$"+o'f3t&!#5$"*j-%pe!"*7$$"+D6?"y&!#5$"+P_G<e!#57$$"1*****\*f"p#e!#;$"+y8Vld!#57$$"+(Rv7)e!#5$"+c4#)4d!#57$$"+m,I/f!#5$"1auQY))G"p&!#;7$$"+N\KFf!#5$"+l=5xc!#57$$",&=#3T&f!#6$"19gY#=_rm&!#;7$$"+-:*3)f!#5$"+d[Ilc!#57$$",NC*f/g!#6$"0Kc$)RZ6n&!#:7$$"+&)pIGg!#5$"+Qu[%o&!#57$$"+Q"=V0'!#5$"1*4YQ%433d!#;7$$"+"HH.3'!#5$"*>q6u&!"*7$$"+Co')Hh!#5$"+-?zHe!#57$$"+XSb"='!#5$"+D/daf!#57$$"*0>!Hi!"*$"+l[,#4'!#57$$"1*****pY;-G'!#;$"+$*))\bi!#57$$"+'>'RLj!#5$"*AX)Hk!"*7$$"+1$*ozj!#5$"+e)*yul!#57$$"+NroHk!#5$"1******)\UPr'!#;7$$"+%yR8['!#5$"+-*R&Go!#57$$"+/eg1l!#5$"0Nx3DK<(o!#:7$$"+C=(=`'!#5$"1,++(p+c!p!#;7$$",v*zJcl!#6$"0z&H7J?Hp!#:7$$"+rTw!e'!#5$"*6EP%p!"*7$$"1****\xu!zg'!#;$"1DJyM@T\p!#;7$$"+%y]]j'!#5$"1,++t-jWp!#;7$$"+^-Wfm!#5$"1b$Q^E$4Kp!#;7$$"+=(HQo'!#5$"+,pf7p!#57$$"1*****zk6ft'!#;$"+PPV_o!#57$$"+=c5$y'!#5$"1******oxO%y'!#;7$$"+&3,Z$o!#5$"+)Glvq'!#57$$"+2%[K)o!#5$"+Xa+Xm!#57$$",XP@'3p!#6$"1\*)fhQ#)>m!#;7$$"+UV*R$p!#5$"+dUk,m!#57$$",b0,)ep!#6$"1k')4Y"4=f'!#;7$$"+pxg$)p!#5$"+cey!f'!#57$$",05y&4q!#6$"1o38+g'**f'!#;7$$"1,++K%[b.(!#;$"+#44-i'!#57$$"1,+]W4cgq!#;$"10O*eJU/l'!#;7$$"1,++dMd&3(!#;$"+d%47p'!#57$$"+w7tOr!#5$"1,++<w(f!o!#;7$$"+#[lu=(!#5$"1,++f$pj&p!#;7$$"*&\3Ms!"*$"+ith=r!#57$$"+:h^(G(!#5$"*\<,K(!"*7$$"+$f0`L(!#5$"1*****fDm8](!#;7$$"*9fiQ(!"*$"+XNB"o(!#57$$"+'=G]V(!#5$"+oEzFy!#57$$"+X*z"*[(!#5$"+Jap[z!#57$$"+mci7v!#5$"1/?U;p%\)z!#;7$$"1,++(Qrg`(!#;$"1,++e*\2,)!#;7$$"1,+vRpP\v!#;$"1s&>2%pl?!)!#;7$$",D\#oiv!#6$"1)QgZKAr-)!#;7$$"-DX!))fd(!#7$"09V?`l,.)!#:7$$"+)f$H*e(!#5$"+)\I)H!)!#57$$",&Gna8w!#6$"10<>[*o2-)!#;7$$"1,++f)*zPw!#;$"1*****p0W8+)!#;7$$"1,+]u*GVm(!#;$"1/o/5tEpz!#;7$$"*4e3p(!"*$"+&>6t#z!#57$$"+s$Qmt(!#5$"+w`+Py!#57$$"+knx)y(!#5$"1,++%35)=x!#;7$$"+z)R"Ry!#5$"+-7e0w!#57$$"+&4q%*)y!#5$"+f$30^(!#57$$",biUX"z!#6$"1G+WWI)[Z(!#;7$$"+c^hRz!#5$"+6BU\u!#57$$"-v"ee;&z!#7$"1F!\!GpDTu!#;7$$",v+-P'z!#6$"1:@4hA$fV(!#;7$$"-DLauvz!#7$"0CZ2oyNV(!#:7$$"+f))y()z!#5$"+'e5VV(!#57$$"-D?"33+)!#7$"02O;w%oQu!#:7$$",:QFQ,)!#6$"1ZI:v(yoW(!#;7$$"1,+vUm%o-)!#;$"0$*\%)3o*eu!#:7$$"1,++/f')R!)!#;$"+sD+vu!#57$$"1,++2Dok!)!#;$"1X:*yRdl^(!#;7$$"*6*\*3)!"*$"*s0Cd(!"*7$$"+=dtT")!#5$"+u.<Mx!#57$$"1*****>VA!*=)!#;$"+UFVDz!#57$$"+&4$GT#)!#5$"+VmMs")!#57$$"1,++3(R8H)!#;$"1,+++q*fU)!#;7$$"1,++#[u7M)!#;$"+9(pan)!#57$$"+[:V$R)!#5$"+GR()4*)!#57$$"*6q9W)!"*$"+j8X$3*!#57$$"+Q"pgY)!#5$"1n2w9Qo^"*!#;7$$"1*****f;o1\)!#;$"+`J'Q?*!#57$$"1***\-H[U])!#;$"17guwrND#*!#;7$$"1****\9%Gy^)!#;$"1lT8HkXT#*!#;7$$"1***\(Q&39`)!#;$"1*oDnP`?D*!#;7$$"1*****Hm))\a)!#;$"1,++=!zqD*!#;7$$"+aVGd&)!#5$"1&3Eb=)zc#*!#;7$$"+X+ep&)!#5$"1UhHcB$>D*!#;7$$"+Od(=e)!#5$"1#H9^%f^U#*!#;7$$"+F9<%f)!#5$"+&=6'G#*!#57$$",Ns?$>')!#6$"1"[n_o+m=*!#;7$$"*-qWk)!"*$"+;8NF"*!#57$$"+(QAcp)!#5$"+RKyg*)!#57$$"+n8kU()!#5$"+bf@n()!#57$$"*3iFz)!"*$"1,++"*=hS&)!#;7$$"+m7]U))!#5$"+2%49K)!#57$$"+Qnq&*))!#5$"+*Hf^7)!#57$$",&*\#=>*)!#6$"06-(GZef!)!#:7$$"+h#eE%*)!#5$"+/Tk5!)!#57$$"1,++R8?c*)!#;$"0hls^+4*z!#:7$$"1,++<Wup*)!#;$"1&GX9+yy(z!#;7$$"1,++cf^w*)!#;$"1.WbOE+uz!#;7$$"1,++&\(G$)*)!#;$"1h<`m5%>(z!#;7$$"+M!f+**)!#5$"1pRe[Btrz!#;7$$"+t0$o**)!#5$"+XFTtz!#57$$"1*****p:_!4!*!#;$"19[U7DL")z!#;7$$"+TPF@!*!#5$"1bj$yQ%o&*z!#;7$$"+D`\L!*!#5$"1y(p-m1m,)!#;7$$"+4prX!*!#5$"1,++uH?W!)!#;7$$",b9-*p!*!#6$"1nZ9CNr=")!#;7$$"+#Q(3%4*!#5$"1******[!z'>#)!#;7$$"+"=,h9*!#5$"+3CCB&)!#57$$"+#QD$)>*!#5$"+$\'3L*)!#57$$"+y;%eC*!#5$"+BR1u$*!#57$$"+p=I'H*!#5$"*ry!z)*!"*7$$"+&3YbM*!#5$"+c$)pO5!"*7$$"+Ot#*)R*!#5$"*[!f$3"!")7$$"+bp6X%*!#5$"*n\W6"!")7$$"+'=U;Z*!#5$"2KVSB&*\k7"!#;7$$"+<u;)\*!#5$"*/"QL6!")7$$"1,]i%>,W]*!#;$"2;zWfl,U8"!#;7$$"-Ds\j5&*!#7$"29BebX(pM6!#;7$$".v)\(oo^*!#8$"2_Ze%e0'[8"!#;7$$",v_-J_*!#6$"2#e^I.LoM6!#;7$$".D^IO$H&*!#8$"2P]uxDeT8"!#;7$$"-v#3qb`*!#7$"1D)ysAyK8"!#:7$$".v.'Q!=a*!#8$"2NaFXEO?8"!#;7$$"+Qw.[&*!#5$"+ycUI6!"*7$$",X!>ts&*!#6$"2)H?')R;I?6!#;7$$"+rhU(f*!#5$"*&=%R5"!")7$$"1*******)R&ok*!#;$"+d)>90"!"*7$$"+OsE(p*!#5$"+l6`(p*!#57$$"+Me)Rs*!#5$"1GjpaOv\"*!#;7$$"+KWq](*!#5$"+lvtC&)!#57$$"+rF?v(*!#5$"1Xi#o)[l')y!#;7$$"*6,(*z*!"*$"+iR)**=(!#57$$"+:T)Q#)*!#5$"1kvQ+\/\k!#;7$$"*7n![)*!"*$"+0-8gc!#57$$",lN=R()*!#6$"1XQXY"R+x%!#;7$$"1,++$fp(**)*!#;$"+H[,RQ!#57$$"*bkb#**!"*$"1JB1nbOxG!#;7$$"1*****p]f8&**!#;$"+*)4v"*=!#57$$",Nvzc(**!#6$"0/11+"R'[*!#;7$$"#5!""$"*>a'om!#;-%&COLORG6'%$RGBG$")C)eq%!")$""!!""$"('>!\&!")-%+_ATTRIBUTEG6#/%'sourceG%,mathdefaultG-%%VIEWG6$;$""!!""$"#5!""%(DEFAULTG-&%&_AXISG6#"""6'-%+_GRIDLINESG6&-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#""!-%*THICKNESSG6#""!-%-TRANSPARENCYG6#$""!!""-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#""!-%*THICKNESSG6#""!-%-TRANSPARENCYG6#$""!!""-&%&_AXISG6#""#6'-%+_GRIDLINESG6&-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#""!-%*THICKNESSG6#""!-%-TRANSPARENCYG6#$""!!""-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#""!-%*THICKNESSG6#""!-%-TRANSPARENCYG6#$""!!""-%+AXESLABELSG6$-I#miG6#/I+modulenameG6"I,TypesettingGI(_syslibG6"65Q"x6"/%'familyGQ!6"/%%sizeGQ#106"/%%boldGQ&false6"/%'italicGQ%true6"/%*underlineGQ&false6"/%*subscriptGQ&false6"/%,superscriptGQ&false6"/%+foregroundGQ([0,0,0]6"/%+backgroundGQ.[255,255,255]6"/%'opaqueGQ&false6"/%+executableGQ&false6"/%)readonlyGQ&false6"/%)composedGQ&false6"/%*convertedGQ&false6"/%+imselectedGQ&false6"/%,placeholderGQ&false6"/%6selection-placeholderGQ&false6"/%,mathvariantGQ'italic6"Q!6"-%%ROOTG6'-%)BOUNDS_XG6#$"$5%!""-%)BOUNDS_YG6#$"#]!""-%-BOUNDS_WIDTHG6#$"%5N!""-%.BOUNDS_HEIGHTG6#$"%!)Q!""-%)CHILDRENG6"

Figure 1 Graph of a 20-term partial sum of the Bessel series for 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

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

JSFH