Computing the Kummer function U(a, b, z) for small values of the arguments

Gil Gómez, Amparo; Segura Sala, José Javier; Temme, Nicolaas Maria

doi:10.1016/j.amc.2015.09.047

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2015_1509.05167v1.pdf (265.5Kb)

Identificadores

URI: http://hdl.handle.net/10902/10277

DOI: 10.1016/j.amc.2015.09.047

ISSN: 0096-3003

ISSN: 1873-5649

Fecha

2015-11-15

Derechos

Atribución-NoComercial-SinDerivadas 3.0 España

Publicado en

Applied Mathematics and Computation, Volume 271, 15 November 2015, Pages 532–539

Editorial

Elsevier Inc.

Enlace a la publicación

https://doi.org/10.1016/j.amc.2015.09.047

Resumen/Abstract

Abstract We describe methods for computing the Kummer function U(a, b, z) for small values of z, with special attention to small values of b. For these values of b the connection formula that represents U(a, b, z) as a linear combination of two 1F1-functions needs a limiting procedure. We use the power series of the 1F1-functions and consider the terms for which this limiting procedure is needed. We give recursion relations for higher terms in the expansion, and we consider the derivative U′(a, b, z) as well. We also discuss the performance for small |z| of an asymptotic approximation of the Kummer function in terms of modified Bessel functions.

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