Notes on some identities involving the Riemann Zeta function
Commun. Korean Math. Soc. 2002 Vol. 17, No. 1, 165-173 Printed March 1, 2002
Hyerim Lee, Bo Myoung Ok, and Junesang Choi Pusan National University, Youngsan University, Dongguk University
Abstract : We first review Ramaswami's and 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 $\zeta(s)$ and Apostol's identities given here.
Keywords : Bernoulli numbers and polynomials, Riemann and Hurwitz Zeta functions, Harmonic numbers, Pochhammer symbol, M\"obius function