Hankel's Integral

$$J_m(x)={x^m\over 2^{m-1}\sqrt{\pi}\,\Gamma\left({m+{\textstyle{1\over 2}}}\right)}\int_0^1 \cos(xt)(1-t^2)^{m-1/2}\,dt,$$

where $J_m(x)$ is a Bessel Function of the First Kind and $\Gamma(z)$ is the Gamma Function. Hankel's integral can be derived from Sonine's Integral.

See also Poisson Integral, Sonine's Integral