# 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