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On extensions of Calkin's binomial identities

โœ Scribed by Jun Wang; Zhizheng Zhang


Book ID
104113299
Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
209 KB
Volume
274
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

โœฆ Synopsis


In this note, we compute three summations involving a power function and a partial sum of the binomial coe cients, which are extensions of Calkin's identities.


๐Ÿ“œ SIMILAR VOLUMES


Calkin's binomial identity
โœ M. Hirschhorn ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 116 KB

We give a fairly direct proof of an identity involving powers of sums of binomial coefficients established recently by Neil J. Calkin, and present some associated formulae. I This research was carried out while the author was on leave from UNSW and visiting

A binomial identity related to Calkin's
โœ Zhizheng Zhang ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 140 KB

coefficients.

A Mathematica Version of Zeilberger's Al
โœ Peter Paule; Markus Schorn ๐Ÿ“‚ Article ๐Ÿ“… 1995 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 665 KB

Based on Gosper's algorithm for indefinite hypergeometric summation, Zeilberger's algorithm for proving binomial coefficient identities constitutes a recent breakthrough in symbolic computation. Mathematica implementations of these algorithms are described. Nontrivial examples are given in order to