The Abel-Zeilberger Algorithm
نویسندگان
چکیده
منابع مشابه
The Abel-Zeilberger Algorithm
We use both Abel’s lemma on summation by parts and Zeilberger’s algorithm to find recurrence relations for definite summations. The role of Abel’s lemma can be extended to the case of linear difference operators with polynomial coefficients. This approach can be used to verify and discover identities involving harmonic numbers and derangement numbers. As examples, we use the Abel-Zeilberger alg...
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By looking under the hood of Zeilberger’s algorithm, as simplified by Mohammed and Zeilberger, it is shown that all the classical hypergeometric closed-form evaluations can be discovered ab initio, as well as many “strange” ones of Gosper, Maier, and Gessel and Stanton. The accompanying Maple package FindHypergeometric explains the various miracles that account for the classical evaluations, an...
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For a hypergeometric series ∑ k f(k, a, b, . . . , c) with parameters a, b, . . . , c, Paule has found a variation of Zeilberger’s algorithm to establish recurrence relations involving shifts on the parameters. We consider a more general problem concerning several similar hypergeometric terms f1(k, a, b, . . . , c), f2(k, a, b, . . . , c), . . ., fm(k, a, b, . . . , c). We present an algorithm ...
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We present a systematic method for proving nonterminating basic hypergeometric identities. Assume that k is the summation index. By setting a parameter x to xqn, we may find a recurrence relation of the summation by using the q-Zeilberger algorithm. This method applies to almost all nonterminating basic hypergeometric summation formulas in the book of Gasper and Rahman. Furthermore, by comparin...
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Superficially, this article, dedicated with friendship and admiration to Amitai Regev, has nothing to do with either Polynomial Identity Rings, Representation Theory, or Young tableaux, to all of which he made so many outstanding contributions. But anyone who knows even a little about Amitai Regev’s remarkable and versatile research, would know that both sums (and multi-sums!), and especially i...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2011
ISSN: 1077-8926
DOI: 10.37236/2013