Summable sums of hypergeometric series

Dennis W Stanton

Research output: Chapter in Book/Report/Conference proceedingChapter

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 languageEnglish (US)
Title of host publicationTHEORY AND APPLICATIONS OF SPECIAL FUNCTIONS
EditorsISMAIL MOURAD, ERIK KOELINK
Pages402-410
Number of pages9
StatePublished - Dec 1 2005

Publication series

NameDevelopments in Mathematics
Volume13
ISSN (Print)1389-2177

Fingerprint

Hypergeometric Series
Binomial theorem
Higher Order
Q-analogue
Necessary
Theorem

Cite this

Stanton, D. W. (2005). Summable sums of hypergeometric series. In ISMAIL. MOURAD, & ERIK. KOELINK (Eds.), THEORY AND APPLICATIONS OF SPECIAL FUNCTIONS (pp. 402-410). (Developments in Mathematics; Vol. 13).

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

THEORY AND APPLICATIONS OF SPECIAL FUNCTIONS. ed. / ISMAIL MOURAD; ERIK KOELINK. 2005. p. 402-410 (Developments in Mathematics; Vol. 13).

Research output: Chapter in Book/Report/Conference proceedingChapter

Stanton, DW 2005, Summable sums of hypergeometric series. in ISMAIL MOURAD & ERIK KOELINK (eds), THEORY AND APPLICATIONS OF SPECIAL FUNCTIONS. Developments in Mathematics, vol. 13, pp. 402-410.
Stanton DW. Summable sums of hypergeometric series. In MOURAD ISMAIL, KOELINK ERIK, editors, THEORY AND APPLICATIONS OF SPECIAL FUNCTIONS. 2005. p. 402-410. (Developments in Mathematics).
Stanton, Dennis W. / Summable sums of hypergeometric series. THEORY AND APPLICATIONS OF SPECIAL FUNCTIONS. editor / ISMAIL MOURAD ; ERIK KOELINK. 2005. pp. 402-410 (Developments in Mathematics).
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