Expansions for Some Confluent Hypergeometric Functions

Posted: 22 Jan 2012

See all articles by Karim M. Abadir

Karim M. Abadir

Imperial College Business School

Date Written: January 21, 2012

Abstract

Power series for the parabolic cylinder function, Dv(z), are derived from known addition theorems, thus enabling a more compact and efficient expression of the function. One of the expansions is applied to find an asymptotic approximation for the function as mod v mod to infinity with mod arg(-v) mod (pi). Next, a large-argument (z) asymptotic addition theorem is derived from an integral representation of Dv(z). Before extending this type of summation theorem to the two general confluent hypergeometric functions, motivating mathematical applications to three integration problems are given as examples of the practical usefulness of the formulae.

Suggested Citation

Abadir, Karim M., Expansions for Some Confluent Hypergeometric Functions (January 21, 2012). Available at SSRN: https://ssrn.com/abstract=1989476

Karim M. Abadir (Contact Author)

Imperial College Business School ( email )

South Kensington Campus
Exhibition Road
London SW7 2AZ, SW7 2AZ
United Kingdom

HOME PAGE: http://www3.imperial.ac.uk/portal/page?_pageid=61,629646&_dad=portallive&_schema=PORTALLIVE

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