A curious summation formula in the light of Gamma function and contiguous relation

Salahuddin; Vinesh Kumar

doi:10.26637/mjm303/007

Abstract

The main aim of the present paper is to establish a curious summation formula involving recurrence relation of Gamma function.

Keywords:

Gauss second summation theorem, Recurrence relation, Prudnikov

Mathematics Subject Classification:

33C05, 33C20, 33D15, 33D50, 33D60

Authors Imprint References Funding Related Articles Downloads

Salahuddin P.D.M College of Engineering, Bahadurgarh , Haryana, India.
Vinesh Kumar Jawaharlal Nehru University, New Delhi, India.

Pages: 289-295
Date Published: 01-07-2015
Vol. 3 No. 03 (2015): Malaya Journal of Matematik (MJM)

Andrews, L.C.(1992) ; Special Function of Mathematics for Engineers,second Edition, McGraw-Hill Co Inc., New York.

Arora, Asish, Singh, Rahul , Salahuddin. ; Development of a family of summation formulae of half argument using Gauss and Bailey theorems, Journal of Rajasthan Academy of Physical Sciences., 7(2008), 335-342.

Bells, Richard. Wong, Roderick; Special Functions, A Graduate Text,Cambridge Studies in Advanced Mathematics, 2010. DOI: https://doi.org/10.1017/CBO9780511762543

Prudnikov, A. P., Brychkov, Yu. A. and Marichev, O.I.; Integrals and Series Vol. 3: More Special Functions. Nauka, Moscow, 1986. Translated from the Russian by G.G. Gould, Gordon and Breach Science Publishers, New York, Philadelphia, London, Paris, Montreux, Tokyo, Melbourne, 1990.

Rainville, E. D.; The contiguous function relations for $p F_q$ with applications to Bateman's $J_n^{u, v}$ and Rice's $H_n(zeta, p, v)$, Bull. Amer. Math. Soc., 51(1945), 714-723. DOI: https://doi.org/10.1090/S0002-9904-1945-08425-0

Salahuddin ,Chaudhary, M. P.,Kumar,Vinesh ; A summation formula of half argument collocated with contiguous relation, Global Journal of Science Frontier Research, 1(2012),11-41.

Slater, S.L; Generalized Hypergeometric Functions. Cambridge University press, 1966.