Abstract
Euler's transformation formula for the Gauss hypergeometric function 2F 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 2F 1 (-1) and 3F 2(1) are derived by applying transformations in the Thomae group. Their parameters are also constrained nonlinearly. Several new one-term evaluations of 2F 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
- General Mathematics
- Applied Mathematics