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

The leading asymptotic behaviour of the Humbert functions , , of two variables is found, when the absolute values of the two independent variables become simultaneously large. New integral representations of these functions are given. These are re-expressed as inverse Laplace transformations and the...

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Bibliographic Details
Published in:Integral transforms and special functions Vol. 29; no. 2; pp. 95 - 112
Main Authors: Wald, Sascha, Henkel, Malte
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 01.02.2018
Taylor & Francis Ltd
Subjects:
Asymptotic properties
asymptotics
Humbert function
Hypergeometric functions
Hypergeometric functions in two variables
Independent variables
Integrals
Laplace transforms
Many-body quantum systems
Mathematical analysis
Representations
special functions
Tauberian theorem
ISSN:1065-2469, 1476-8291
Online Access:Get full text
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Summary:The leading asymptotic behaviour of the Humbert functions , , of two variables is found, when the absolute values of the two independent variables become simultaneously 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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ISSN:1065-2469
1476-8291
DOI:10.1080/10652469.2017.1404596