Exponentially small expansions of the confluent hypergeometric functions

Richard B. Paris

Research output: Contribution to journalArticle

3 Citations (Scopus)
19 Downloads (Pure)

Abstract

The asymptotic expansions of the confluent hypergeometric functions 1F1(a; b; z) and U(a, b, z) are examined as |z|→∞ on the Stokes lines arg z = ±π. Particular attention is given to the exponentially small contributions associated with these two functions. Numerical results demonstrating the accuracy of the expansions are given.
Original languageEnglish
Pages (from-to)6601-6609
Number of pages9
JournalApplied Mathematical Sciences
Volume7
Issue number133
DOIs
Publication statusPublished - 2013

Fingerprint

Confluent Hypergeometric Function
Stokes
Asymptotic Expansion
Numerical Results
Line

Cite this

@article{281ab2f6c4c74c20bf243ca5224fd4ca,
title = "Exponentially small expansions of the confluent hypergeometric functions",
abstract = "The asymptotic expansions of the confluent hypergeometric functions 1F1(a; b; z) and U(a, b, z) are examined as |z|→∞ on the Stokes lines arg z = ±π. Particular attention is given to the exponentially small contributions associated with these two functions. Numerical results demonstrating the accuracy of the expansions are given.",
author = "Paris, {Richard B.}",
year = "2013",
doi = "10.12988/ams.2013.310559",
language = "English",
volume = "7",
pages = "6601--6609",
journal = "Applied Mathematical Sciences",
issn = "1314-7552",
number = "133",

}

Exponentially small expansions of the confluent hypergeometric functions. / Paris, Richard B.

In: Applied Mathematical Sciences, Vol. 7, No. 133, 2013, p. 6601-6609.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Exponentially small expansions of the confluent hypergeometric functions

AU - Paris, Richard B.

PY - 2013

Y1 - 2013

N2 - The asymptotic expansions of the confluent hypergeometric functions 1F1(a; b; z) and U(a, b, z) are examined as |z|→∞ on the Stokes lines arg z = ±π. Particular attention is given to the exponentially small contributions associated with these two functions. Numerical results demonstrating the accuracy of the expansions are given.

AB - The asymptotic expansions of the confluent hypergeometric functions 1F1(a; b; z) and U(a, b, z) are examined as |z|→∞ on the Stokes lines arg z = ±π. Particular attention is given to the exponentially small contributions associated with these two functions. Numerical results demonstrating the accuracy of the expansions are given.

U2 - 10.12988/ams.2013.310559

DO - 10.12988/ams.2013.310559

M3 - Article

VL - 7

SP - 6601

EP - 6609

JO - Applied Mathematical Sciences

JF - Applied Mathematical Sciences

SN - 1314-7552

IS - 133

ER -