Numerische Mathematik

, Volume 116, Issue 2, pp 269–289 | Cite as

Asymptotics and numerics of polynomials used in Tricomi and Buchholz expansions of Kummer functions

Article

Abstract

Expansions in terms of Bessel functions are considered of the Kummer function 1F1(a; c, z) (or confluent hypergeometric function) as given by Tricomi and Buchholz. The coefficients of these expansions are polynomials in the parameters of the Kummer function and the asymptotic behavior of these polynomials for large degree is given. Tables are given to show the rate of approximation of the asymptotic estimates. The numerical performance of the expansions is discussed together with the numerical stability of recurrence relations to compute the polynomials. The asymptotic character of the expansions is explained for large values of the parameter a of the Kummer function.

Keywords

Kummer functions Confluent hypergeometric functions Bessel functions Asymptotic expansions Computation of special functions 

Mathematics Subject Classification (2000)

33C10 33C15 41A30 41A60 65D20 

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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Departamento de Ingeniería Matemática e InformáticaUniversidad Pública de NavarraPamplonaSpain
  2. 2.Centrum Wiskunde & InformaticaAmsterdamThe Netherlands

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