Contiguous relations and their computations for 2F1 hypergeometric series

Adel K. Ibrahim, Medhat A. Rakha

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

The hypergeometric function 2F1 [a1, a2 ; a3 ; z] plays an important role in mathematical analysis and its application. Gauss defined two hypergeometric functions to be contiguous if they have the same power-series variable, if two of the parameters are pairwise equal, and if the third pair differs by ±1. He showed that a hypergeometric function and any two other contiguous to it are linearly related. In this paper, we present an interesting formula as a linear relation of three shifted Gauss polynomials in the three parameters a1, a2 and a3. More precisely, we obtained a recurrence relation including 2F1 [a1 + α1, a2 ; a3 ; z], 2F1 [a1, a2 + α2 ; a3 ; z] and 2F1 [a1, a2 ; a3 + α3 ; z] for any arbitrary integers α1, α2 and α3.

Original languageEnglish
Pages (from-to)1918-1926
Number of pages9
JournalComputers and Mathematics with Applications
Volume56
Issue number8
DOIs
Publication statusPublished - Oct 2008

Fingerprint

Hypergeometric Series
Hypergeometric Functions
Gauss
Linear Relation
Recurrence relation
Mathematical Analysis
Power series
Pairwise
Linearly
Polynomials
Polynomial
Integer
Arbitrary

Keywords

  • F hypergeometric function
  • Computer algebra
  • Contiguous function relation
  • Gauss hypergeometric function
  • Linear recurrence relation

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Modelling and Simulation

Cite this

Contiguous relations and their computations for 2F1 hypergeometric series. / Ibrahim, Adel K.; Rakha, Medhat A.

In: Computers and Mathematics with Applications, Vol. 56, No. 8, 10.2008, p. 1918-1926.

Research output: Contribution to journalArticle

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