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.
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