East Asian mathematical journal
- Volume 18 Issue 1
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- Pages.111-125
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- 2002
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- 1226-6973(pISSN)
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- 2287-2833(eISSN)
SOME FAMILIES OF INFINITE SERIES SUMMABLE VIA FRACTIONAL CALCULUS OPERATORS
- Tu, Shih-Tong (Department of Mathematics Chung Yuan Christian University, Taiwan) ;
- Wang, Pin-Yu (Department of Mechanical Engineering Nan-Ya Institute of Technology, Taiwan) ;
- Srivastava, H.M. (Department of Mathematics and Statistics University of Victoria, Canada)
- Published : 2002.06.27
Abstract
Many different families of infinite series were recently observed to be summable in closed forms by means of certain operators of fractional calculus(that is, calculus of integrals and derivatives of any arbitrary real or complex order). In this sequel to some of these recent investigations, the authors present yet another instance of applications of certain fractional calculus operators. Alternative derivations without using these fractional calculus operators are shown to lead naturally a family of analogous infinite sums involving hypergeometric functions.
Keywords
- fractional calculus;
- infinite series;
- Riemann-Liouville operator;
- fractional derivative;
- fractional integral;
- generalized Leibniz rule;
- hypergeometric functions;
- expansion formula;
- reduction formula;
- fractional differintegral operators;
- Hurwitz-Lerch Zeta function;
- summation formulas