INFINITE SERIES WITH HARMONIC NUMBERS AND CENTRAL BINOMIAL COEFFICIENTS-Reference-Cited by-同舟云学术

INFINITE SERIES WITH HARMONIC NUMBERS AND CENTRAL BINOMIAL COEFFICIENTS

Published:2009-05 Issue:03 Volume:05 Page:429-448
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

CHU WENCHANG¹,ZHENG DEYIN²

Affiliation:

1. Dipartimento di Matematica, Università del Salento, Lecce-Arnesano P. O. Box 193, 73100 Lecce, Italy

2. Department of Mathematics, Hangzhou Normal University, Hangzhou 310036, P. R. China

Abstract

By means of two hypergeometric summation formulae, we establish two large classes of infinite series identities with harmonic numbers and central binomial coefficients. Up to now, these numerous formulae have hidden behind very few known identities of Apéry-like series for Riemann-zeta function, discovered mainly by Lehmer [14] and Elsner [12] as well as Borwein et al. [4, 5, 7]. All the computation and verification are carried out by an appropriately-devised Mathematica package.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042109002171

Reference21 articles.

1. Borwein and Bradley's Apérv-Like Formulae for ζ(4n + 3)

2. Ramanujan’s Notebooks

3. Central Binomial Sums, Multiple Clausen Values, and Zeta Values

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