The Sine Integral - Maple Help

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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

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)

See Also

ChiSquare, combinat[Chi], convert/Ei, Ei, inifcns, Li, simplify[Ei]

References

  

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


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