Asymptotics of the Humbert functions ${\Psi }_1$ and ${\Psi }_2$

Abstract

A compilation of new results on the asymptotic behaviour of the Humbert functions ${\Psi }_1$ and ${\Psi }_2$, and also on the Appell function $F_2$, is presented. As a by-product, we confirm a conjectured limit which appeared recently in the study of the $1D$ Glauber-Ising model. We also propose two elementary asymptotic methods and confirm through some illustrative examples that both methods have great potential and can be applied to a large class of problems of asymptotic analysis. Finally, some directions of future research are pointed out in order to suggest ideas for further study.

20 pages

References in corpus (2)

• On integral representations and asymptotics of some hypergeometric functions in two variables
• Finite-size scaling in the ageing dynamics of the $1D$ Glauber-Ising model