Binomial sums involving harmonic numbers
Open Access
- 1 April 2011
- journal article
- Published by Walter de Gruyter GmbH in Mathematica Slovaca
- Vol. 61 (2), 215-226
- https://doi.org/10.2478/s12175-011-0006-5
Abstract
This paper develops the approach to the evaluation of a class of infinite series that involve special products of binomial type, generalized harmonic numbers of order 1 and rational functions. We give new summation results for certain infinite series of non-hypergeometric type. New formulas for the number π are included.Keywords
This publication has 11 references indexed in Scilit:
- Mathematics by ExperimentPublished by Taylor & Francis Ltd ,2008
- On the irrationality of polynomial Cantor seriesActa Arithmetica, 2008
- On the irrationality of factorial seriesActa Arithmetica, 2005
- On the irrationality of Cantor seriesJournal für die reine und angewandte Mathematik (Crelles Journal), 2004
- Simultaneous Generation of Koecher and Almkvist-Granville's Apéry-Like FormulaeExperimental Mathematics, 2004
- Some New Formulas for πExperimental Mathematics, 2003
- Central Binomial Sums, Multiple Clausen Values, and Zeta ValuesExperimental Mathematics, 2001
- A Class of Series Acceleration Formulae for Catalan's ConstantThe Ramanujan Journal, 1999
- A Simple Proof of the Irrationality of π 4The American Mathematical Monthly, 1986
- Interesting Series Involving the Central Binomial CoefficientThe American Mathematical Monthly, 1985