# Integral sine

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The special function defined for real by For one has One sometimes uses the notation Some particular values are: Some special relations:   where is the integral cosine. For small, The asymptotic representation for large is where  The integral sine has the series representation (*)

As a function of the complex variable , , defined by (*), is an entire function of in the -plane.

The integral sine is related to the integral exponential function by See also Si-ci-spiral.

For references, and the graph of the integral sine, see Integral cosine.

#### Comments

This function is better known as the sine integral.

How to Cite This Entry:
Integral sine. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Integral_sine&oldid=11622
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article