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Poisson Integral

A.k.a. Bessel's Second Integral.

J_n(z)={\left({1\over 2}\right)^n\over \Gamma(n+{\textstyle{...
...r 2}})}\int_0^\pi \cos(z\cos\theta )\sin^{2n}\theta \,d\theta,

where $J_n(z)$ is a Bessel Function of the First Kind and $\Gamma(x)$ is a Gamma Function. It can be derived from Sonine's Integral. With $n=0$, the integral becomes Parseval's Integral.

See also Bessel Function of the First Kind, Parseval's Integral, Sonine's Integral

© 1996-9 Eric W. Weisstein