ON A HYPERGEOMETRIC SUMMATION THEOREM DUE TO QURESHI ET AL. Choi, Junesang; Rathie, Arjun K.;
We first aim at proving an interesting easily derivable summation formula. Then it is easily seen that this formula immediately yields a hypergeometric summation theorem recently added to the literature by Qureshi et al. Moreover we apply the main formulas to present some interesting summation formulas, whose special cases are also seen to yield the earlier known results.
gamma function;Pochhammer symbol;hypergeometric function;generalized hypergeometric function;Chebyshev polynomials of the first and second kind;Jacobi polynomials;
W. N. Bailey, Products of generalized hypergeometric series, Proc. London Math. Soc. 28 (1928), no. 2, 242-254.
J. Choi, Notes on formal manipulations of double series, Commun. Korean Math. Soc. 18 (2003), no. 4, 781-789.
A. Erdelyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher Transcendental Functions, Vol. 2, McGraw-Hill Book Company, New York, Toronto and London, 1953.
A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series, Vol. 3; More Special Functions, "Nauka", Moscow, 1986 (in Russian); Translated from the Russian by G. G. Gould, Gordon and Breach Science Publishers, New York, Philadelphia, London, Paris, Montreux and Melbourne, 1990.
M. I. Qureshi, K. Quraishi, and H. M. Srivastava, Some hypergeometric summation for-mulas and series identities associated with exponential and trigonometric functions, Integral Transforms Spec. Funct. 19 (2008), no. 3-4, 267-276.
E. D. Rainville, Special Functions, Macmillan Company, New York, 1960; Reprinted by Chelsea Publishing Company, Bronx, New York, 1971.
H. M. Srivastava and J. Choi, Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Science Publishers, Amsterdam, London and New York, 2012.
H. M. Srivastava and H. L. Manocha, A Treatise on Generating Functions, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto, 1984.