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

Khristo N. Boyadzhiev

Published 2009-12-29, updated 2009-12-31Version 2

It is shown that the curious identity of Simons follows immediately from Euler's series transformation formula and also from an identity due to Ljunggren. The relation of Simons' identity to Legendre's polynomials is also discussed. At the end we use the generalized Euler series transformation to obtain two recent binomial identities of Munarini.