On Stirling numbers and Euler sums

The article is published in Journal of Computational and Applied Mathematics, 79(1997),119--130. 
  • Abstract

  • In this paper, we propose the another yet generalization of Stirling numbers of the first kind for non-integer values of their arguments. We discuss the analytic representations of Stirling numbers through harmonic numbers, the generalized hypergeometric function and the logarithmic beta integral. We present then infinite series involving Stirling numbers and demonstrate how they are related to Euler sums. Finally we derive the closed form for the multiple zeta function $\zeta(p,1,\ldots,1)$ for $p>1$.
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  • Please send corrections to Victor S. Adamchik
    Computer Science Department, 
    Carnegie Mellon University, Pittsburgh, PA.