Probabilistic proof of a Hankel transform of Laguerre polynomials

This paper shows that the Hankel transform of order ν may be interpreted as a mixture formulation of a function with the non-central gamma as mixing distribution. This result is applied to give a probabilistic derivation of the Hankel transform of order ν of generalized Laguerre polynomials. The application of this result to numerically evaluate the Hankel transform or a Hankel-type integral by the Monte Carlo method is also briefly examined.