Some infinite series and functional relations that arose in the context of fractional calculus

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Title:	Some infinite series and functional relations that arose in the context of fractional calculus
Authors:	Chen, Kung-yu;陳功宇;Srivastava, H. M.
Contributors:	淡江大學數學學系
Keywords:	fractional calculus;Psi (or Digamma) functions;generalized hypergeometric functions;functional relations;H-functions;Mellin–Barnes contour integral
Date:	2000-12-01
Issue Date:	2010-01-28 07:15:39 (UTC+8)
Publisher:	Elsevier
Abstract:	Several interesting infinite series relations were derived recently by applying such operators of fractional calculus as the familiar Riemann–Liouville fractional differintegral operator 0Dμz of (real or complex) order μ. The main object of this paper is to present much simpler alternative derivations of substantially more general families of infinite series relations without using fractional calculus. Some relevant connections among various known results are also provided.
Relation:	Journal of Mathematical Analysis and Applications 252(1), pp.376-388
DOI:	10.1006/jmaa.2000.7079
Appears in Collections:	[Graduate Institute & Department of Mathematics] Journal Article

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