# Integral sine

From Encyclopedia of Mathematics

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. A.B. Ivanov (originator),

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Integral_sine&oldid=11622

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098