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Title
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A generalization of Kummer's identity
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Author
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Abstract
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| The well-known formula of Kummer evaluates the hypergeometric series F-2(1) ((A,B)(C) \ -1) when the relation C - A + B = 1 holds. This paper deals with the evaluation of F-2(1) (- 1) series in the case when C - A + B is an integer. Such a series is expressed as a sum of two Gamma-terms multiplied by terminating F-3(2)(1) series. A few such formulas were essentially known to Whipple in the 1920s. Here we give a simpler and more complete overview of this type of evaluation. Additionally, algorithmic aspects of evaluating hypergeometric series are considered. We illustrate Zeilberger's method and discuss its applicability to nonterminating series and present a couple of similar generalizations of other known formulas. |
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Language
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English
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Source (journal)
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The Rocky Mountain journal of mathematics. - Provo, Utah
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Source (book)
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NATO Advanced-Study-Institute/National-Science-Foundation Conference on, Special Functions, MAY 29-JUN 09, 2000, ARIZONA STATE UNIV, TEMPE, ARIZONA
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Publication
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Provo, Utah
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2002
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ISSN
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0035-7596
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Volume/pages
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32
:2
(2002)
, p. 919-936
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ISI
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000178733800026
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Full text (Publisher's DOI)
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Full text (open access)
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