Sonine's Integral

$$J_m(x) = {2x^{m-n}\over 2^{m-n}\Gamma(m-n)} \int^1_0 J_n(xt)t^{n+1}(1-t^2)^{m-n-1}\,dt,$$

where $J_m(x)$ is a Bessel Function of the First Kind and $\Gamma(x)$ is the Gamma Function.

See also Hankel's Integral, Poisson Integral