An algorithmic proof theory for hypergeometric (ordinary and <Emphasis Type="Italic">q </Emphasis>) multisum/integral identities
نویسندگان
چکیده
It is shown that every 'proper-hypergeometric ' multisum/integral identity, or q-identity, with a fixed number of summations and/or integration signs, possesses a short, computer-constructible proof. We give a fast algorithm for finding such proofs. Most of the identities that involve the classical special functions of mathematical physics are readily reducible to the kind of identities treated here. We give many examples of the method, including computer-generated proofs of identities of Mehta-Dyson, Selberg, Hille-Hardy, q-Saalsch/itz, and others. The prospect of using the method for proving multivariate identities that involve an arbitrary number of summations/integrations is discussed.
منابع مشابه
RATIONAL FUNCTION CERTIFICATION OF MULTISUM / INTEGRAL / “ q ” IDENTITIES
The method of rational function certification for proving terminating hypergeometric identities is extended from single sums or integrals to multi-integral/sums and “q” integral/sums.
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