### Abstract

The aim of this research note is to prove the following new transformation formula (1 - x)^{-2a} _{3}F_{2} [ _{c + 3/2, d} ^{a, a + 1/2, d + 1}; x^{2}/(1 - x)_{2} ] = _{4}F_{3} [ _{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 = √16d^{2} - 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 language | English |
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Pages (from-to) | 207-209 |

Number of pages | 3 |

Journal | Mathematical Communications |

Volume | 14 |

Issue number | 2 |

Publication status | Published - Dec 2009 |

### 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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## Cite this

Rakha, M. A., Rathie, N., & Chopra, P. (2009). On an extension of a quadratic transformation formula due to Kummer.

*Mathematical Communications*,*14*(2), 207-209.