A Binomial Coefficient Identity Associated to a Conjecture of Beukers
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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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In this note we shall prove the following curious identity of sums of powers of the partial sum of binomial coefficients.
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 1998
ISSN: 1077-8926
DOI: 10.37236/1348