On Stirling Numbers and Euler Sums
نویسنده
چکیده
In this paper, we propose the another yet generalization of Stirling numbers of the rst 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 in nite series involving Stirling numbers and demonstrate how they are related to Euler sums. Finally we derive the closed form for the multiple zeta function (p; 1; : : : ; 1) for p > 1.
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