Asymptotic expansion of the Wright function for large variable and parameter (2110.06690v1)

Abstract: We consider the asymptotic expansion of the Wright function [W_{\lambda,\mu}(z)=\sum_{n=0}^\infty\frac{z^n}{n! \Gamma(\lambda n+\mu)}\qquad (\lambda>-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.