### Abstract

A simple proof is given of a new summation formula recently added in the literature for a terminating

_{r + 3}*F*_{r + 2}(1) hypergeometric series for the case when*r*pairs of numeratorial and denominatorial parameters differ by positive integers. This formula represents an extension of the well-known Saalschütz summation formula for a_{3}*F*_{2}(1) series. Two applications of this extended summation formula are discussed. The first application extends two identities given by Ramanujan and the second, which also employs a similar extension of the Vandermonde–Chu summation theorem for the_{2}*F*_{1}series, extends certain reduction formulas for the Kampé de Fériet function of two variables given by Exton and Cvijović & Miller.Original language | English |
---|---|

Pages (from-to) | 4891-4900 |

Number of pages | 10 |

Journal | Mathematical Methods in the Applied Sciences |

Volume | 38 |

Issue number | 18 |

Early online date | 6 Mar 2015 |

DOIs | |

Publication status | Published - Dec 2015 |

## Fingerprint Dive into the research topics of 'An alternative proof of the extended Saalschütz summation theorem for the <sub>r + 3</sub>F<sub>r + 2</sub>(1) series with applications'. Together they form a unique fingerprint.

## Cite this

Kim, Y. S., Rathie, A. K., & Paris, R. B. (2015). An alternative proof of the extended Saalschütz summation theorem for the

_{r + 3}F_{r + 2}(1) series with applications.*Mathematical Methods in the Applied Sciences*,*38*(18), 4891-4900. https://doi.org/10.1002/mma.3408