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The Euler Series Transformation and the Binomial Identities of Ljunggren, Munarini and Simons
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Khristo N. Boyadzhiev
Published/Copyright:
July 8, 2010
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
Received: 2009-08-31
Accepted: 2010-02-15
Published Online: 2010-07-08
Published in Print: 2010-July
© de Gruyter 2010
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Articles in the same Issue
- Corrigendum and Statement on Priority for: Conjugacy Classes and Class Number
- The Euler Series Transformation and the Binomial Identities of Ljunggren, Munarini and Simons
- A Multitude of Expressions for the Stirling Numbers of the First Kind
- Infinitely Often Dense Bases for the Integers with a Prescribed Representation Function
- A Note on the Exact Expected Length of the kth Part of a Random Partition
- On Congruence Conditions for Primality
- The Divisibility of an – bn by Powers of n
- Long Arithmetic Progressions in Small Sumsets
- On the Least Common Multiple of Q-Binomial Coefficients
- Flat Cyclotomic Polynomials of Order Four and Higher
- On Vanishing Sums of Distinct Roots of Unity
Keywords for this article
Binomial identity;
Euler series transformation;
Ljunggren identity;
Simons' identity;
Legendre polynomials
Articles in the same Issue
- Corrigendum and Statement on Priority for: Conjugacy Classes and Class Number
- The Euler Series Transformation and the Binomial Identities of Ljunggren, Munarini and Simons
- A Multitude of Expressions for the Stirling Numbers of the First Kind
- Infinitely Often Dense Bases for the Integers with a Prescribed Representation Function
- A Note on the Exact Expected Length of the kth Part of a Random Partition
- On Congruence Conditions for Primality
- The Divisibility of an – bn by Powers of n
- Long Arithmetic Progressions in Small Sumsets
- On the Least Common Multiple of Q-Binomial Coefficients
- Flat Cyclotomic Polynomials of Order Four and Higher
- On Vanishing Sums of Distinct Roots of Unity
