NOTES ON SOME IDENTITIES INVOLVING THE RIEMANN ZETA FUNCTION Lee, Hye-Rim; Ok, Bo-Myoung; Choi, June-Sang;
We first review Ramaswami's find Apostol's identities involving the Zeta function in a rather detailed manner. We then present corrected, or generalized formulas, or a different method of proof for some of them. We also give closed-form evaluation of some series involving the Riemann Zeta function by an integral representation of ζ(s) and Apostol's identities given here.
Bernoulli numbers and polynomials;Riemann and Hurwitz Zeta functions;Harmonic numbers;Pochhammer symbol;Mobius function;