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On integral representations and asymptotics of some hypergeometric functions in two variables (1707.06275v2)
Published 19 Jul 2017 in math-ph, cond-mat.stat-mech, hep-th, math.CA, and math.MP
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.
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