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

Sascha Wald, Malte Henkel

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)
11 Downloads (Pure)

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.
Original languageEnglish
Pages (from-to)95-112
Number of pages18
JournalJournal Integral Transforms and Special Functions
Volume29
Issue number2
Early online date24 Nov 2017
DOIs
Publication statusE-pub ahead of print - 24 Nov 2017
Externally publishedYes

Bibliographical note

This is an Accepted Manuscript of an article published by Taylor & Francis in [Journal Title] on 24/11/207 available online: http://www.tandfonline.com/10.1080/10652469.2017.1404596

Copyright © and Moral Rights are retained by the author(s) and/ or other copyright owners. A copy can be downloaded for personal non-commercial research or study, without prior permission or charge. This item cannot be reproduced or quoted extensively from without first obtaining permission in writing from the copyright holder(s). The content must not be changed in any way or sold commercially in any format or medium without the formal permission of the copyright holders.

Keywords

  • Hypergeometric functions in two variables
  • Humbert function
  • asymptotics
  • special functions
  • Tauberian theorem
  • Many-body quantum systems

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