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A class of generalized hypergeometric summations

✍ Scribed by Allen R. Miller

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
263 KB
Volume
87
Category
Article
ISSN
0377-0427

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✦ Synopsis

Summations over the positive integers n of the generalized hypergeometric expressions (_+ 1)"pFp+ 1 [-n2x2] (X > 0) are derived in closed form. The specialization p = 0, for example, reduces to known results for Schl6milch series. In addition, we record the apparently not readily available sine and cosine transforms of pFp + 1 [-bZx2] (b > 0), the latter of which is used together with a form of the Poisson summation formula to deduce the aforementioned results.

πŸ“œ SIMILAR VOLUMES

Certain summation and transformation for
Certain summation and transformation formulas for generalized hypergeometric series
✍ Allen R. Miller πŸ“‚ Article πŸ“… 2009 πŸ› Elsevier Science 🌐 English βš– 487 KB

We derive summation formulas for generalized hypergeometric series of unit argument, one of which upon specialization reduces to Minton's summation theorem. As an application we deduce a reduction formula for a certain KampΓ© de FΓ©riet function that in turn provides a Kummer-type transformation formu