East Asian mathematical journal
- Volume 17 Issue 1
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- Pages.135-146
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- 2001
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- 1226-6973(pISSN)
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- 2287-2833(eISSN)
SOME FAMILIES OF INFINITE SUMS DERIVED BY MEANS OF FRACTIONAL CALCULUS
- Romero, Susana Salinas De (Centro de Investigacion de Matematica Aplicada Facultad de Ingenieria La Universidad del Zulia, Venezuela) ;
- Srivastava, H.M. (Department of Mathematics and Statistics University of Victoria, Canada)
- Published : 2001.06.25
Abstract
Several families of infinite series were summed recently by means of certain operators of fractional calculus(that is, calculus of derivatives and integrals of any real or complex order). In the present sequel to this recent work, it is shown that much more general classes of infinite sums can be evaluated without using fractional calculus. Some other related results are also considered.
Keywords
- fractional calculus;
- infinite series;
- Riemann-Liouville operator;
- fractional derivative;
- fractional integral;
- generalized Leibniz rule;
- hypergeometric functions;
- expansion formula;
- reduction formula