On integral representations and asymptotics of some hypergeometric functions in two variables

Abstract

The leading asymptotic behaviour of the Humbert functions ${\Phi }_2$, ${\Phi }_3$, ${\Xi }_2$ of two variables is found, when the absolute values of the two independent variables become simultaneosly 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.

17 pages

References in corpus (1)

• A massive Feynman integral and some reduction relations for Appell functions

Cited by in corpus (1)

• Lindblad dynamics of the quantum spherical model