### Abstract

New expansions for certain 2F _{l}'s as a sum of r higher order hypergeometric series are given. When specialized to the binomial theorem, these r hypergeometric series sum. The results represent cubic and higher order transformations, and only Vandermonde's theorem is necessary for the elementary proof. Some q-analogues are also given.

Original language | English (US) |
---|---|

Title of host publication | THEORY AND APPLICATIONS OF SPECIAL FUNCTIONS |

Editors | ISMAIL MOURAD, ERIK KOELINK |

Pages | 402-410 |

Number of pages | 9 |

State | Published - Dec 1 2005 |

### Publication series

Name | Developments in Mathematics |
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Volume | 13 |

ISSN (Print) | 1389-2177 |

### Fingerprint

### Cite this

*THEORY AND APPLICATIONS OF SPECIAL FUNCTIONS*(pp. 402-410). (Developments in Mathematics; Vol. 13).

**Summable sums of hypergeometric series.** / Stanton, Dennis W.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*THEORY AND APPLICATIONS OF SPECIAL FUNCTIONS.*Developments in Mathematics, vol. 13, pp. 402-410.

}

TY - CHAP

T1 - Summable sums of hypergeometric series

AU - Stanton, Dennis W

PY - 2005/12/1

Y1 - 2005/12/1

N2 - New expansions for certain 2F l's as a sum of r higher order hypergeometric series are given. When specialized to the binomial theorem, these r hypergeometric series sum. The results represent cubic and higher order transformations, and only Vandermonde's theorem is necessary for the elementary proof. Some q-analogues are also given.

AB - New expansions for certain 2F l's as a sum of r higher order hypergeometric series are given. When specialized to the binomial theorem, these r hypergeometric series sum. The results represent cubic and higher order transformations, and only Vandermonde's theorem is necessary for the elementary proof. Some q-analogues are also given.

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M3 - Chapter

AN - SCOPUS:84859482773

SN - 0387242317

SN - 9780387242316

T3 - Developments in Mathematics

SP - 402

EP - 410

BT - THEORY AND APPLICATIONS OF SPECIAL FUNCTIONS

A2 - MOURAD, ISMAIL

A2 - KOELINK, ERIK

ER -