Applications of a certain family of hypergeometric summation formulas associated with Psi and Zeta functions
Commun. Korean Math. Soc. 2001 Vol. 16, No. 2, 319-332
Junesang Choi, H. M. Srivastava, Yongsup Kim
Dongguk University, University of Victoria, Wonkwang University
Abstract : The main object of this paper is first to give two contiguous analogues of a well-known hypergeometric summation formula for ${}_2 F_{1}(1/2)$. We then apply each of these analogues with a view to evaluating the sums of several classes of series in terms of the Psi (or Digamma) and the Zeta functions. Relevant connections of the series identities presented here with those given elsewhere are also pointed out.
Keywords : Polygamma functions, Psi (or Digamma) function, Riemann Zeta function, Hurwitz Zeta function, Hypergeometric series, Stirling numbers
MSC numbers : Primary 40-00; Secondary 33B15, 33C05
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