# Integral hyperbolic sine

From Encyclopedia of Mathematics

The special function defined, for real , by

where is the integral sine. The integral hyperbolic sine can be represented by the series

It is related to the integral hyperbolic cosine by

where is the integral logarithm.

Sometimes it is denoted by .

For references see Integral cosine.

#### Comments

This function, which is seldom used because of its relation with the sine integral, is also called the hyperbolic sine integral. It can, of course, be defined (as above) for .

**How to Cite This Entry:**

Integral hyperbolic sine.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Integral_hyperbolic_sine&oldid=11472

This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article