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.
Bibliographical noteThis 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
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- Hypergeometric functions in two variables
- Humbert function
- special functions
- Tauberian theorem
- Many-body quantum systems