On some combinatorial identities and harmonic sums

Author:

Batir Necdet1

Affiliation:

1. Department of Mathematics, Nevşehir HBV University, Nevşehir, 50300, Turkey

Abstract

For any [Formula: see text] we first give new proofs for the following well-known combinatorial identities [Formula: see text] and [Formula: see text] and then we produce the generating function and an integral representation for [Formula: see text]. Using them we evaluate many interesting finite and infinite harmonic sums in closed form. For example, we show that [Formula: see text] and [Formula: see text] where [Formula: see text] are generalized harmonic numbers defined below.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

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