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The Euler Series Transformation and the Binomial Identities of Ljunggren, Munarini and Simons

Khristo N. Boyadzhiev
Published Online: 2010-07-08 | DOI: https://doi.org/10.1515/integ.2010.022

Abstract

We point out that the curious identity of Simons follows immediately from Euler's series transformation formula and also from an identity due to Ljunggren. We also mention its relation to Legendre's polynomials. At the end we use the generalized Euler series transformation to obtain two recent binomial identities of Munarini.

Keywords.: Binomial identity; Euler series transformation; Ljunggren identity; Simons' identity; Legendre polynomials

About the article

Received: 2009-08-31

Accepted: 2010-02-15

Published Online: 2010-07-08

Published in Print: 2010-07-01


Citation Information: Integers, Volume 10, Issue 3, Pages 265–271, ISSN (Print) 1867-0652, DOI: https://doi.org/10.1515/integ.2010.022.

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