Identities for the Riemann Zeta Function
نویسنده
چکیده
In this paper, we obtain several expansions for ζ(s) involving a sequence of polynomials in s, denoted by αk(s). These polynomials can be regarded as a generalization of Stirling numbers of the first kind and our identities extend some series expansions for the zeta function that are known for integer values of s. The expansions also give a different approach to the analytic continuation of the Riemann zeta function. The inspiration for our formulas comes from Kenter’s short note in the May 1999 Monthly [K] where he derives a formula for Euler’s constant γ which can be regarded as the s → 0 case of (1.8), after subtracting 1/s from both sides. We start with Riemann’s formula
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