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

摘要

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 twoindependent variables become simultaneosly large. New integral representationsof these functions are given. These are re-expressed as inverse Laplacetransformations and the asymptotics is then found from a Tauberian theorem.Some integrals of the Humbert functions are also analysed.