Integral and computational representation of summation which extends a Ramanujan's sum

Authors

  • Tibor K. Pogány Faculty of Maritime Studies, University of Rijeka, Rijeka 51000, Croatia Author
  • Arjun K. Rathie Department of Mathematics, School of Mathematical and Physical Sciences, Central University of Kerala, Kasaragod – 671 328, Kerala, India Author
  • Shoukat Ali Department of Mathematics, Govt. Engineering College Bikaner, Bikaner – 334 005, Rajasthan State, India Author

Keywords:

Ramanujan's summation formula, generalized hypergeometric functions ${}_pF_q$, Mellin-Barnes type path integral, Hurwitz-Lerch Zeta function, computational representation

Subjects:

33C20, 40H05

Abstract

A generalized sum, which contains Ramanujan'ssummation formula recorded in Hardy's article [G.H. Hardy, Achapter from Ramanujan's notebook, Proc. Camb. Phil. Soc. 21 (1923), 492–503] as a special case, has been represented inthe form of Mellin-Barnes type contour integral. A computationalrepresentation formula is derived for this summation in terms ofthe unified Hurwitz-Lerch Zeta function.

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Published

2012-07-15

Issue

Vol. 64 No. 3 (2012): Vol. 64, Issue 3

Section

Articles

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Copyright (c) 2012 Authors retain copyright to their work.

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This work is licensed under a Creative Commons Attribution 4.0 International License.