On an extension of a quadratic transformation formula due to Kummer

Medhat A. Rakha, Navratna Rathie, Purnima Chopra

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

The aim of this research note is to prove the following new transformation formula (1 - x)-2a 3F2 [ c + 3/2, d a, a + 1/2, d + 1; x2/(1 - x)2 ] = 4F3 [ 2c + 2, 2d + 1/2A - 1/2, 2d - 1/2A - 1/2 2a, c, 2d + 1/2A +1/2, 2d - 1/2A + 1/2; 2x ] valid for |x| <1/2 and if |x| = 1/2, then Re(c - 2a) > 0, where A = √16d2 - 16cd - 8d + 1. For d = c + 1/2, we get quadratic transformations due to Kummer. The result is derived with the help of the generalized Gauss's summation theorem available in the literature.

Original languageEnglish
Pages (from-to)207-209
Number of pages3
JournalMathematical Communications
Volume14
Issue number2
Publication statusPublished - Dec 2009

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Keywords

  • Gauss summation theorem
  • Kummer transformation
  • Quadratic transformation formula

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Analysis
  • Applied Mathematics
  • Geometry and Topology

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