On the computations of contiguous relations for 2F1 hypergeometric series

Medhat A. Rakha, Adel K. Ibrahim, Arjun K. Rathie

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Contiguous relations for hypergeometric series contain an enormous amount of hidden information. Applications of contiguous relations range from the evaluation of hypergeometric series to the derivation of summation and transformation formulas for such series. In this paper, a general formula joining three Gauss functions of the form 2F1[a1, a2; a3; z] with arbitrary integer shifts is presented. Our analysis depends on using shifted operators attached to the three parameters a1, a2 and a3. We also, discussed the existence condition of our formula.

Original languageEnglish
Pages (from-to)291-302
Number of pages12
JournalCommunications of the Korean Mathematical Society
Volume24
Issue number2
DOIs
Publication statusPublished - 2009

Fingerprint

Hypergeometric Series
Joining
Transformation Formula
Summation Formula
Gauss
Integer
Series
Evaluation
Arbitrary
Operator
Range of data
Form

Keywords

  • Contiguous relations
  • Hypergeometric function

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

On the computations of contiguous relations for 2F1 hypergeometric series. / Rakha, Medhat A.; Ibrahim, Adel K.; Rathie, Arjun K.

In: Communications of the Korean Mathematical Society, Vol. 24, No. 2, 2009, p. 291-302.

Research output: Contribution to journalArticle

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