Asymptotic expansion of the Wright function for large variable and parameter

Abstract

We consider the asymptotic expansion of the Wright function \[W_{λ,μ}(z)=\sum_{n=0}^\infty\frac{z^n}{n! Γ(λn+μ)}\qquad (λ>-1)\] for large (positive and negative) variable and large parameter $\mu$. The analysis is based on use of the method of steepest descents applied to a suitable integral representation and, in part, complements the recent work of Ansari and Askari. Numerical results are presented to illustrate the accuracy of the different expansions obtained.

10 pages, 5 figures