## Abstract

Euler's transformation formula for the Gauss hypergeometric function _{2}F _{1} is extended to hypergeometric functions of higher order. Unusually, the generalized transformation constrains the hypergeometric function parameters algebraically but not linearly. Its consequences for hypergeometric summation are explored. It has as a corollary a summation formula of Slater. From this formula new one-term evaluations of _{2}F _{1} (-1) and _{3}F _{2}(1) are derived by applying transformations in the Thomae group. Their parameters are also constrained nonlinearly. Several new one-term evaluations of _{2}F _{1}(-1) with linearly constrained parameters are derived as well.

Original language | English (US) |
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Pages (from-to) | 39-57 |

Number of pages | 19 |

Journal | Transactions of the American Mathematical Society |

Volume | 358 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2006 |

## ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics