Lauricella and Humbert functions through probabilistic tools
Jean-François Chamayou, Jacek Wesołowski · Integral Transforms and Special Functions · 2009
New integral formulas for the Humbert Φ2 function and for the Lauricella F A and F D functions are derived. The basic tools are neutrality properties of the probability Dirichlet distribution, the Laplace transform of which is the Humbert Φ2 function.