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On Stirling Numbers and Euler Sums

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journal contribution
posted on 01.01.1973, 00:00 by Victor S. Adamchik
In this paper, we propose another yet generalization of Stirling numbers of the first kind for noninteger 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 ζ(p, 1,…, 1) for Re(p)>1.


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