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

2007/10/22 by Donal F. Connon, Connon, Donal F. · 4 citations
Mathematics · #11M06 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #History and Overview (math.HO)

paper · pdf · doi:10.48550/arxiv.0710.4022

openalex publication_date 2007/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Torus Knot complements: A natural series for the natural logarithm
• Six Gluon Open Superstring Disk Amplitude, Multiple Hypergeometric Series and Euler-Zagier Sums
• Riemann Zeta Function
• The Positivity of a Sequence of Numbers and the Riemann Hypothesis

Cited by

• The Relationship Between Euler Numbers and Bernoulli Numbers with Ordered Partitions
• An introduction to the Bernoulli function
• Some applications of the sine and cosine integrals
• Fourier series representations of the logarithms of the Euler gamma function and the Barnes multiple gamma functions

Related

• Some series and integrals involving the Riemann zeta function, binomial coefficients and the harmonic numbers. Volume II(a)
• Some series and integrals involving the Riemann zeta function, binomial coefficients and the harmonic numbers. Volume II(b)
• Some series and integrals involving the Riemann zeta function, binomial coefficients and the harmonic numbers. Volume VI
• Some series and integrals involving the Riemann zeta function, binomial coefficients and the harmonic numbers. Volume III
• Some series and integrals involving the Riemann zeta function, binomial coefficients and the harmonic numbers. Volume V