Representation of Formal Power Series - Maple Programming Help

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Representation of Formal Power Series

 

Calling Sequence

Description

Examples

Calling Sequence

function(arguments)

Description

• 

Formal power series are procedures that return the coefficients of the power series they represent. Thus namei is the coefficient of xi in the series called name.

• 

The values of the coefficients are saved using a remember table, so all computed coefficients can be seen via op(4, op(name)).

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The actual procedure is identical for all power series; the only differences are the general term and the values that each remembers.

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The general term of the power series can be obtained via name(_k) .

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Note: that each intermediate power series created in a calculation should be named.

Examples

withpowseries:

powcreateen=1n!,e0=1:

powcreatefn=fn1n2fn2,f0=1,f1=5,f2=2:

tpsforme,x,6

1+x+12x2+16x3+124x4+1120x5+Ox6

(1)

tpsformf,x,6

1+5x+2x2+245x3+1720x4+1800x5+Ox6

(2)

Compute the series  f^e .

logfpowlogf:

elogfmultiplye,logf:

resultpowexpelogf:

tpsformresult,x,6

1+5x+7x2+76745x3+2351240x4+39231800x5+Ox6

(3)

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