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
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.
This function is better known as the sine integral.
Integral sine. A.B. Ivanov (originator), Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Integral_sine&oldid=11622