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Si

The Sine Integral

Ci

The Cosine Integral

Ssi

The Shifted Sine Integral

Shi

The Hyperbolic Sine Integral

Chi

The Hyperbolic Cosine Integral

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

Si(x)

Ci(x)

Ssi(x)

Shi(x)

Chi(x)

Parameters

x

-

expression

Description

• 

These integrals are defined for all complex x as follows:

Six=∫0xsinttⅆt

Cix=γ+lnx+0xcost1tⅆt

Ssix=Sixπ2

Shix=∫0xsinhttⅆt

Chix=γ+lnx+0xcosht1tⅆt

• 

The functions Si, Ssi, and Shi are entire.  The functions Ci and Chi have a logarithmic singularity at the origin and have a branch cut along the negative real axis.

Examples

Ci1.

0.3374039229

(1)

Ci3

Ci3

(2)

evalf

0.1196297860

(3)

Si3.14159+7.6I

63.60695388123.1816272I

(4)

Ssi12345.67890

0.00005756635677

(5)

Si12345.67890

1.570738760

(6)

Shiπ

Shiπ

(7)

Chi1.+I

0.8821721806+1.283547193I

(8)

convertCix,Ei

12Ei1,Ix12Ei1,Ix+12Icsgnx1csgnIxπ

(9)

References

  

Abramowitz, M. and Stegun, I., eds. Handbook of Mathematical Functions. New York: Dover, 1972.

See Also

ChiSquare

combinat[Chi]

convert/Ei

Ei

inifcns

Li

simplify[Ei]

 


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