A Binomial Coefficient Identity Associated with Beukers' Conjecture on Apéry numbers
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چکیده
منابع مشابه
A Binomial Coefficient Identity Associated to a Conjecture of Beukers
Remark. This identity is easily verified using the WZ method, in a generalized form [Z] that applies when the summand is a hypergeometric term times a WZ potential function. It holds for all positive n, since it holds for n=1,2,3 (check!), and since the sequence defined by the sum satisfies a certain (homog.) third order linear recurrence equation. To find the recurrence, and its proof, downloa...
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By means of partial fraction decomposition, an algebraic identity on rational function is established. Its limiting case leads us to a harmonic number identity, which in turn has been shown to imply Beukers’ conjecture on the congruence of Apéry numbers. Throughout this work, we shall use the following standard notation: Harmonic numbers H0 = 0 and Hn = ∑n k=1 1/k Shifted factorials (x)0 = 1 an...
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Let q be regarded as either a complex number q ∈ C or a p-adic number q ∈ Cp. If q ∈ C, then we always assume |q| < 1. If q ∈ Cp, we normally assume |1− q|p < p − 1 p−1 , which implies that q = exp(x log q) for |x|p ≤ 1. Here, | · |p is the p-adic absolute value in Cp with |p|p = 1 p . The q-basic natural number are defined by [n]q = 1−q 1−q = 1 + q + · · · + q , ( n ∈ N), and q-factorial are a...
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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], ...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2004
ISSN: 1077-8926
DOI: 10.37236/1856