Summation Formulas Involving Binomial Coefficients, Harmonic Numbers, and Generalized Harmonic Numbers

Finite summation formulas involving binomial coefficients, harmonic numbers and generalized harmonic numbers

A variety of identities involving harmonic numbers and generalized harmonic numbers have been investigated since the distant past and involved in a wide range of diverse fields such as analysis of algorithms in computer science, various branches of number theory, elementary particle physics and theoretical physics. Here we show how one can obtain further interesting identities about certain fin...

Some summation formulas involving harmonic numbers and generalized harmonic numbers

Summation formulae involving harmonic numbers

Several summation formulae for finite and infinite series involving the classical harmonic numbers are presented. The classical harmonic numbers are defined by

Harmonic Numbers and Cubed Binomial Coefficients

Anthony Sofo Victoria University College, Victoria University, P.O. Box 14428, Melbourne City, VIC 8001, Australia Correspondence should be addressed to Anthony Sofo, [email protected] Received 18 January 2011; Accepted 3 April 2011 Academic Editor: Toufik Mansour Copyright q 2011 Anthony Sofo. This is an open access article distributed under the Creative Commons Attribution License, which...

Series with Central Binomial Coefficients, Catalan Numbers, and Harmonic Numbers

We present several generating functions for sequences involving the central binomial coefficients and the harmonic numbers. In particular, we obtain the generating functions for the sequences ( 2n n ) Hn, ( 2n n ) 1 nHn, ( 2n n ) 1 n+1Hn , and ( 2n n ) n m. The technique is based on a special Euler-type series transformation formula.