On integral representations and asymptotics of some hypergeometric functions in two variables. (arXiv:1707.06275v2 [math-ph] UPDATED)

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. 查看全文>>