Partial Fractions and q-Binomial Determinant Identities
نویسندگان
چکیده
منابع مشابه
Partial Fractions and q-Binomial Determinant Identities
Partial fraction decomposition method is applied to evaluate a general determinant of shifted factorial fractions, which contains several Gaussian binomial determinant identities .
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We give some identities involving sums of powers of the partial sum of q-binomial coefficients, which are q-analogues of Hirschhorn’s identities [Discrete Math. 159 (1996), 273–278] and Zhang’s identity [Discrete Math. 196 (1999), 291–298].
متن کاملThe q-Binomial Theorem and two Symmetric q-Identities
We notice two symmetric q-identities, which are special cases of the transformations of 2φ1 series in Gasper and Rahman’s book (Basic Hypergeometric Series, Cambridge University Press, 1990, p. 241). In this paper, we give combinatorial proofs of these two identities and the q-binomial theorem by using conjugation of 2-modular diagrams.
متن کاملCOMPUTATION OF q-PARTIAL FRACTIONS
We study a special partial fraction technique which is designed for rational functions with poles on the unit circle, known as q-fractions. Even though the theory of q-partial fractions has already been applied to the Rademacher Conjecture, no systematic computational development appeared. In this paper we present two algorithms for the computation of q-partial fractions and highlight certain p...
متن کاملHybrid Proofs of the q-Binomial Theorem and Other Identities
We give “hybrid” proofs of the q-binomial theorem and other identities. The proofs are “hybrid” in the sense that we use partition arguments to prove a restricted version of the theorem, and then use analytic methods (in the form of the Identity Theorem) to prove the full version. We prove three somewhat unusual summation formulae, and use these to give hybrid proofs of a number of identities d...
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ژورنال
عنوان ژورنال: Cubo (Temuco)
سال: 2010
ISSN: 0719-0646
DOI: 10.4067/s0719-06462010000300001