The expansion of the confluent hypergeometric function on the positive real axis

R. B. Paris

doi:10.12988/ams.2018.712351

The expansion of the confluent hypergeometric function on the positive real axis

R. B. Paris

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Abstract

The asymptotic expansion of the Kummer function ₁F₁(a; b; z) is examined as z → +∞ on the Stokes line arg z = 0. The correct form of the subdominant algebraic contribution is obtained for non-integer a. Numerical results demonstrating the accuracy of the expansion are given.

Original language	English
Pages (from-to)	19-26
Number of pages	8
Journal	Applied Mathematical Sciences
Volume	12
Issue number	1
DOIs	https://doi.org/10.12988/ams.2018.712351
Publication status	Published - 5 Jan 2018

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10.12988/ams.2018.712351Licence: CC BY

Paris_TheExpansionOfTheConfluentHypergeometricFunctionOnThePositiveRealAxis_Published_2018Final published version, 228 KBLicence: CC BY

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abstract = "The asymptotic expansion of the Kummer function 1F1(a; b; z) is examined as z → +∞ on the Stokes line arg z = 0. The correct form of the subdominant algebraic contribution is obtained for non-integer a. Numerical results demonstrating the accuracy of the expansion are given.",

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AB - The asymptotic expansion of the Kummer function 1F1(a; b; z) is examined as z → +∞ on the Stokes line arg z = 0. The correct form of the subdominant algebraic contribution is obtained for non-integer a. Numerical results demonstrating the accuracy of the expansion are given.

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The expansion of the confluent hypergeometric function on the positive real axis

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