J an 2 00 4 Preprint ( 2004 - 01 - 07 ) AN EXTENSION OF A CURIOUS BINOMIAL IDENTITY
نویسندگان
چکیده
In 2002 Z. W. Sun published a curious identity involving binomial coefficients. In this paper we present the following generalization of the identity: (x + (m + 1)z) m n=0 (−1) n x + y + nz m − n y + n(z + 1) n =z 0lnm (−1) n n l x + l m − n (1 + z) n+l (1 − z) n−l + (x − m) x m .
منابع مشابه
On Various Combinatorial Sums and Related Identities
In this talk we give a survey of results and methods on some combinatorial sums involving binomial coefficients and related to Bernoulli and Euler polynomials. We will also talk about certain sums of minima and maxima related to Dedekind sums. Some interesting identities associated with the various sums will also be introduced. 1. A curious identity and the sum ∑ k≡r (mod m) ( n k ) In 1988 Zhi...
متن کاملA curious binomial identity
In this note we shall prove the following curious identity of sums of powers of the partial sum of binomial coefficients.
متن کاملCombinatorial Proof of a Curious q-Binomial Coefficient Identity
q-binomial coefficient identity Victor J. W. Guo and Jiang Zeng Department of Mathematics, East China Normal University, Shanghai 200062, People’s Republic of China [email protected], http://math.ecnu.edu.cn/~jwguo Université de Lyon; Université Lyon 1; Institut Camille Jordan, UMR 5208 du CNRS; 43, boulevard du 11 novembre 1918, F-69622 Villeurbanne Cedex, France [email protected], ...
متن کاملAnother Proof of an Extension of a Curious Identity
. (1) In 2002 Z. W. Sun [7] proved the case when z = 1 using double recursion. Later four alternative proofs have been provided for the special case. A generating function proof was given by A. Panholzer and H. Prodinger [6]; D. Merlini and R. Sprugnoli [5] established it through Riordan arrays; S. B. Ekhad and M. Mohammed [4] proved it based on a WZ method. Later, W. Chu and L. V. D. Claudio [...
متن کاملJ ul 2 00 9 Preprint , arXiv : 0810 . 0467 LINEAR EXTENSION OF THE ERDŐS - HEILBRONN CONJECTURE
The famous Erd˝ os-Heilbronn conjecture plays an important role in the development of additive combinatorics. In 2007 Z. W. Sun made the following further conjecture (which is the linear extension of the Erd˝ os-Heilbronn conjecture): For any finite subset A of a field F and nonzero elements a where p(F) is the additive order of the multiplicative identity of F , and δ ∈ {0, 1} takes the value ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004