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Calkin's binomial identity

✍ Scribed by M. Hirschhorn

Book ID
103061416
Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
116 KB
Volume
159
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

✦ Synopsis

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

πŸ“œ SIMILAR VOLUMES

A binomial identity related to Calkin's
A binomial identity related to Calkin's
✍ Zhizheng Zhang πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 140 KB

coefficients.

On extensions of Calkin's binomial ident
On extensions of Calkin's binomial identities
✍ Jun Wang; Zhizheng Zhang πŸ“‚ Article πŸ“… 2004 πŸ› Elsevier Science 🌐 English βš– 209 KB

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.

A curious binomial identity
A curious binomial identity
✍ Neil J. Calkin πŸ“‚ Article πŸ“… 1994 πŸ› Elsevier Science 🌐 English βš– 98 KB

In this communication we shall prove a curious identity of sums of powers of the partial sum of binomial coefficients. An identity ## Theorem. C;=O (~~_o(~))3=n23"-1+23"-~2"(~). Proof. Definef,=C;=, (Ci=O(k"))3. It is sufficient to show that Write A,=C:=,(,"). Then fn=C;=oA:.