On integral representations and asymptotics of some hypergeometric functions in two variables - Wald, Sascha; Henkel, Malte (Integral transforms and special functions, 2018)
The leading asymptotic behaviour of the Humbert functions , , of two variables is found, when the absolute values of the two independent variables become simultaneously large. New integral representations of these functions are given. These are re-expressed as inverse Laplace transformations and the asymptotics is then found from a Tauberian theorem. Some integrals of the Humbert functions are also analysed.