Exponentially small expansions of the confluent hypergeometric functions

Richard B. Paris

Research output: Contribution to journal › Article

3 Citations (Scopus)
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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 languageEnglish
Pages (from-to)6601-6609
Number of pages9
JournalApplied Mathematical Sciences
Volume7
Issue number133
DOIs
Publication statusPublished - 2013

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Confluent Hypergeometric Function
Stokes
Asymptotic Expansion
Numerical Results
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Paris, Richard B. / Exponentially small expansions of the confluent hypergeometric functions. In: Applied Mathematical Sciences. 2013 ; Vol. 7, No. 133. pp. 6601-6609.
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Paris, RB 2013, 'Exponentially small expansions of the confluent hypergeometric functions', Applied Mathematical Sciences, vol. 7, no. 133, pp. 6601-6609. https://doi.org/10.12988/ams.2013.310559

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 journal › Article

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

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JO - Applied Mathematical Sciences

JF - Applied Mathematical Sciences

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IS - 133

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Paris RB. Exponentially small expansions of the confluent hypergeometric functions. Applied Mathematical Sciences. 2013;7(133):6601-6609. https://doi.org/10.12988/ams.2013.310559

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