Abstract
The leading asymptotic behaviour of the Humbert functions Φ2, Φ3, Ξ2 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 language | English |
|---|---|
| Pages (from-to) | 95-112 |
| Number of pages | 18 |
| Journal | Integral Transforms and Special Functions |
| Volume | 29 |
| Issue number | 2 |
| Early online date | 24 Nov 2017 |
| DOIs | |
| Publication status | Published - 2018 |
| Externally published | Yes |
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/10.1080/10652469.2017.1404596Copyright © 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