Exponentially small expansions in the asymptotics of the Wright function

Authors:
R. B. Paris
Affiliations:
Division of Complex Systems, University of Abertay Dundee, Dundee DD1 1HG, UK
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

Citing 2
Cited 1

The asymptotic expansion of a generalised incomplete gamma function

Journal of Computational and Applied Mathematics
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,

Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,

The discrete analogue of Laplace's method

Computers & Mathematics with Applications

Quantified Score

Hi-index	7.29

Visualization

Abstract

We consider exponentially small expansions present in the asymptotics of the generalised hypergeometric function, or Wright function, "p@J"q(z) for large |z| that have not been considered in the existing theory. Our interest is principally with those functions of this class that possess either a finite algebraic expansion or no such expansion and with parameter values that produce exponentially small expansions in the neighbourhood of the negative real z axis. Numerical examples are presented to demonstrate the presence of these exponentially small expansions.