Generalization of Kummer's second theorem with applications

Yong Sup Kim, M. A. Rakha, A. K. Rathie

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

The aim of this research paper is to obtain single series expression for i = 0, ±1, ±2, ±3, ±4, ±5, where 1F1(·) is the function of Kummer. For i = 0, we have the well known Kummer second theorem. The results are derived with the help of generalized Gauss second summation theorem obtained earlier by Lavoie et al. In addition to this, explicit expressions of each for i = 0, ±1, ±2, ±3, ±4, ±5 are also given. For i = 0, we get two interesting and known results recorded in the literature. As an applications of our results, explicit expressions for i, j = 0, ±1, ±2, ±3, ±4, ±5 and for j = 0, ±1, ±2, ±3, ±4, ±5 are given. For i = j = 0 and j = 0, we respectively get the well known Preece identity and a well known quadratic transformation formula due to Kummer. The results derived in this paper are simple, interesting, easily established and may be useful in the applicable sciences.

Original languageEnglish
Pages (from-to)387-402
Number of pages16
JournalComputational Mathematics and Mathematical Physics
Volume50
Issue number3
DOIs
Publication statusPublished - 2010

Keywords

  • Dixon theorem
  • Function of Kummer
  • Generalization of Kummer theorem
  • Generalized gipergeometric function
  • Hypergeometric Gauss summation theorem

ASJC Scopus subject areas

  • Computational Mathematics

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