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Some results involving series representations of hypergeometric functions

โœ Scribed by M.W. Coffey; S.J. Johnston

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
416 KB
Volume
233
Category
Article
ISSN
0377-0427

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โœฆ Synopsis

In this paper, we prove some generalisations of several theorems given in [K.A. Driver, S.J. Johnston, An integral representation of some hypergeometric functions, Electron. Trans. Numer. Anal. 25 (2006) 115-120] and examine some special cases which correspond to a transformation given by Chaundy in [T.W. Chaundy, An extension of hypergeometric functions, I., Quart. J. Maths. Oxford Ser. 14 (1943) and other transformations involving the Riemann zeta function and the beta function.

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On some series representations of the Hurwitz zeta function
โœ Mark W. Coffey ๐Ÿ“‚ Article ๐Ÿ“… 2008 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 153 KB

A variety of infinite series representations for the Hurwitz zeta function are obtained. Particular cases recover known results, while others are new. Specialization of the series representations apply to the Riemann zeta function, leading to additional results. The method is briefly extended to the