where is a Bessel function of the first kind and is the gamma function. Hankel's integral can be derived from Sonine's integral.
Hankel's Integral
See also
Poisson Integral, Sonine's IntegralExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Hankel's Integral." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HankelsIntegral.html