Integral sine
From Encyclopedia of Mathematics
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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://encyclopediaofmath.org/index.php?title=Integral_sine&oldid=11622
Integral sine. Encyclopedia of Mathematics. URL: http://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