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