### Abstract

_{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 |

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### Cite this

_{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

}

_{r + 3}F

_{r + 2}(1) series with applications',

*Mathematical Methods in the Applied Sciences*, vol. 38, no. 18, pp. 4891-4900. https://doi.org/10.1002/mma.3408

**An alternative proof of the extended Saalschütz summation theorem for the _{r + 3}F_{r + 2}(1) series with applications.** / Kim, Yong S.; Rathie, Arjun K.; Paris, Richard B.

Research output: Contribution to journal › Article

TY - JOUR

T1 - An alternative proof of the extended Saalschütz summation theorem for the r + 3Fr + 2(1) series with applications

AU - Kim, Yong S.

AU - Rathie, Arjun K.

AU - Paris, Richard B.

PY - 2015/12

Y1 - 2015/12

N2 - A simple proof is given of a new summation formula recently added in the literature for a terminating r + 3Fr + 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 3F2(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 2F1 series, extends certain reduction formulas for the Kampé de Fériet function of two variables given by Exton and Cvijović & Miller.

AB - A simple proof is given of a new summation formula recently added in the literature for a terminating r + 3Fr + 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 3F2(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 2F1 series, extends certain reduction formulas for the Kampé de Fériet function of two variables given by Exton and Cvijović & Miller.

U2 - 10.1002/mma.3408

DO - 10.1002/mma.3408

M3 - Article

VL - 38

SP - 4891

EP - 4900

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

SN - 0170-4214

IS - 18

ER -

_{r + 3}F

_{r + 2}(1) series with applications. Mathematical Methods in the Applied Sciences. 2015 Dec;38(18):4891-4900. https://doi.org/10.1002/mma.3408