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A certain family of series associated with the zeta and related functions. (English) Zbl 1160.11339
Summary: The history of problems of evaluation of series associated with the Riemann Zeta function can be traced back to Christian Goldbach (1690–1764) and Leonhard Euler (1707–1783). Many different techniques to evaluate various series involving the Zeta and related functions have since then been developed. The authors show how elegantly certain families of series involving the Zeta function can be evaluated by starting with a single known identity for the generalized (or Hurwitz) Zeta function. Some special cases and their connections with already developed series involving the Zeta and related functions are also considered

MSC:
11M06 \(\zeta (s)\) and \(L(s, \chi)\)
11M35 Hurwitz and Lerch zeta functions
33B15 Gamma, beta and polygamma functions
11B68 Bernoulli and Euler numbers and polynomials
11B73 Bell and Stirling numbers
33E20 Other functions defined by series and integrals
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Full Text: Euclid