Abstract
In this paper, we obtain several expansions for ζ(s) involving a sequence of polynomials in s, denoted by α k (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.
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References
Jordan, C.: Calculus of Finite Differences, 3 edn. Chelsea, New York (1965)
Kenter, F.: A matrix representation for Euler’s constant, γ. Am. Math. Mon. 452–454 (1999)
Rassias, T.M., Srivastava, H.M.: Some classes of infinite series associated with the Riemann Zeta and Polygamma functions and generalized harmonic numbers. Appl. Math. Comput. 131, 593–605 (2002)
Shen, L.: Remarks on some integrals and series involving stirling numbers and ζ(n). Trans. Am. Math. Soc. 347(4), 1391–1399 (1995)
Sloane, N.: The online encyclopedia of integer sequences. www.research.att.com/~njas/sequences/
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Rubinstein, M.O. Identities for the Riemann zeta function. Ramanujan J 27, 29–42 (2012). https://doi.org/10.1007/s11139-010-9276-8
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DOI: https://doi.org/10.1007/s11139-010-9276-8