MATEMATIČKI VESNIK
МАТЕМАТИЧКИ ВЕСНИК



MATEMATIČKI VESNIK
Integral and computational representation of summation which extends a Ramanujan's sum
Tibor K. Pogány, Arjun K. Rathie and Shoukat Ali

Abstract

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

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

MSC: 33C20, 40H05

Pages:  240$-$245     

Volume  64 ,  Issue  3 ,  2012