Some series and integrals involving the Riemann zeta function, binomial coefficients and the harmonic numbers. Volume I

Abstract

In this series of seven papers, predominantly by means of elementary analysis, we establish a number of identities related to the Riemann zeta function. Whilst this paper is mainly expository, some of the formulae reported in it are believed to be new, and the paper may also be of interest specifically due to the fact that most of the various identities have been derived by elementary methods.

This revised paper contains some corrections and some additional material

References in corpus (5)

• Six Gluon Open Superstring Disk Amplitude, Multiple Hypergeometric Series and Euler-Zagier Sums
• Contributions to the Theory of the Barnes Function
• Polygamma theory, the Li/Keiper constants, and validity of the Riemann Hypothesis
• An Infinite Product for e^gamma via Hypergeometric Formulas for Euler's Constant, gamma
• Ramanujan's Approximation to the nth Partial Sum of the Harmonic Series

Cited by in corpus (4)

• Euler-Hurwitz series and non-linear Euler sums
• Elementary evaluations of some Euler sums
• Determination of some generalised Euler sums involving the digamma function
• Euler sums and a prime numbers conundrum