✦ LIBER ✦

A curious binomial identity

✍ Scribed by Neil J. Calkin

Book ID: 103061071
Publisher: Elsevier Science
Year: 1994
Tongue: English
Weight: 98 KB
Volume: 131
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(94)90394-8

No coin nor oath required. For personal study only.

✦ Synopsis

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:.

📜 SIMILAR VOLUMES

A kind of binomial identity

✍ Zhizheng Zhang 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 285 KB

The purpose of this article is to discuss the following sum:

Note on a Binomial Identity

✍ Carlitz, L. 📂 Article 📅 1975 🏛 Society for Industrial and Applied Mathematics 🌐 English ⚖ 186 KB

Calkin's binomial identity

✍ M. Hirschhorn 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 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

✍ Zhizheng Zhang 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 140 KB

coefficients.

Binomial convolutions and hypergeometric

Binomial convolutions and hypergeometric identities

✍ Chu Wenchang 📂 Article 📅 1994 🏛 Springer Milan 🌐 Italian ⚖ 732 KB

Identities from the binomial transform

✍ Kwang-Wu Chen 📂 Article 📅 2007 🏛 Elsevier Science 🌐 English ⚖ 119 KB

A sequence b n is the binomial transform of the sequence a n if b n = n k=0 n k a k . We derive a general identity for such pairs of sequences. Various known identities are obtained as particular cases.