Communications of the
Korean Mathematical Society CKMS

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