Asymptotic analysis of the Wright function with a large parameter

In this paper, using the exponential conformal map for the Hankel contour we show a new Schlafli-type integral representation for the Wright function. We apply the steepest descent method and the Lagrange expansion to find the asymptotic expansions of Wright function for the large parameter. We study two cases for the stationary points and discuss the associated asymptotic expansions. The results extend the asymptotic expansions of the Bessel functions of the first and second kinds. (c) 2021 Elsevier Inc. All rights reserved.

Automated summary

The paper introduces a new Schlafli-type integral representation for the Wright function using the exponential conformal map for the Hankel contour. The asymptotic expansions of the Wright function for large parameters are found using the steepest descent method and Lagrange expansion. The study of stationary points and associated asymptotic expansions extends the asymptotic expansions of the Bessel functions of the first and second kinds.