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arXiv · 1707.06275

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

Sascha Wald·Malte Henkel
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Abstract

The leading asymptotic behaviour of the Humbert functions $Φ_2$, $Φ_3$, $Ξ_2$ 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.

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Sascha Wald, Malte Henkel. 2017-11-09. On integral representations and asymptotics of some hypergeometric functions in two variables. https://doi.org/10.1080/10652469.2017.1404596

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