Exponentially small expansions of the confluent hypergeometric functions

Richard B. Paris

doi:10.12988/ams.2013.310559

Exponentially small expansions of the confluent hypergeometric functions

Richard B. Paris

Research output: Contribution to journal › Article › peer-review

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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 language	English
Pages (from-to)	6601-6609
Number of pages	9
Journal	Applied Mathematical Sciences
Volume	7
Issue number	133
DOIs	https://doi.org/10.12988/ams.2013.310559
Publication status	Published - 2013

Keywords

Confluent hypergeometric functions
Stokes lines
Asymptotic expansions
Exponentially small expansions

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10.12988/ams.2013.310559Licence: CC BY

Paris_ExponentiallySmallExpansionsOfTheConfluentHypergeometricFunctions_Published_2013Final published version, 113 KBLicence: CC BY

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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.

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JO - Applied Mathematical Sciences

JF - Applied Mathematical Sciences

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Exponentially small expansions of the confluent hypergeometric functions

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