UNIFORM ASYMPTOTIC EXPANSIONS FOR HYPERGEOMETRIC FUNCTIONS WITH LARGE PARAMETERS III

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Abstract

In this paper, we discuss asymptotic expansions for the Gauss hypergeometric function (2)F1(a + e(1)lambda, b + e(2)lambda; c + e(3)lambda; z), where e(j) = 0, +/- 1, as vertical bar lambda vertical bar -> infinity. We complete the results of two previous publications, extend the sectors of validity, and give more details on the computation of the coefficients.

Original languageEnglish
Pages (from-to)199-210
Number of pages12
JournalAnalysis and Applications
Volume8
Issue number2
DOIs
Publication statusPublished - Apr 2010

Keywords

  • Hypergeometric function
  • large parameter
  • uniform asymptotic expansions
  • RECURSIONS

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