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Open Access Original research

Euler-related sums

Anthony Sofo

Author Affiliations

Victoria University College, Victoria University, Melbourne City, PO Box 14428, Victoria, 8001, Australia

Mathematical Sciences 2012, 6:10  doi:10.1186/2251-7456-6-10

Published: 9 July 2012

Abstract

Purpose

The purpose of this paper is to develop a set of identities for Euler type sums of products of harmonic numbers and reciprocal binomial coefficients.

Method

We use analytical methods to obtain our results.

Results

We obtain identities for variant Euler sums of the type <a onClick="popup('http://www.iaumath.com/content/6/1/10/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.iaumath.com/content/6/1/10/mathml/M1">View MathML</a>, and its finite counterpart, which generalize some results obtained by other authors.

Conclusions

Identities are successfully achieved for the sums under investigation. Some published results have been successfully generalized.

Keywords:
Harmonic numbers; Binomial coefficients and gamma function; Polygamma function; Combinatorial series identities and summation formulas; Partial fraction approach; MSC (2000); primary: 05A10; 05A19; 11B65; secondary: 11B83; 11M06; 33B15; 33D60; 33C20