Bessel's second integral

There are at least two integrals called the Poisson integral. The first is also known as Bessel's second integral, J_n(z) = (1/2 z)^n/(Γ(n + 1/2) Γ(1/2)) integral_0^π cos(z cos θ) sin^(2n) θ d θ, where J_n(z) is a Bessel function of the first kind and Γ(x) is a gamma function. It can be derived from Sonine's integral. With n = 0, the integral becomes Parseval's integral.

Bessel function of the first kind | circle | harmonic function | Parseval's integral | Poisson kernel | Sonine's integral | sphere