Q-Hypergeometric Series and Their Transformation Formulae
نویسندگان
چکیده
منابع مشابه
Summation Formulae for Noncommutative Hypergeometric Series
Hypergeometric series with noncommutative parameters and argument, in the special case involving square matrices, have recently been studied by a number of researchers including (in alphabetical order) Durán, Duval, Grünbaum, Iliev, Ovsienko, Pacharoni, Tirao, and others. See [3, 6, 8, 9, 10, 11, 12, 16] for some selected papers. The subject of hypergeometric series involving matrices is closel...
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Abstract. We study multivariable (bilateral) basic hypergeometric series associated with (type A) Macdonald polynomials. We derive several transformation and summation properties for such series, including analogues of Heine’s 2φ1 transformation, the q-Pfaff-Kummer and Euler transformations, the q-Saalschütz summation formula, and Sear’s transformation for terminating, balanced 4φ3 series. For ...
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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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ژورنال
عنوان ژورنال: International Journal for Research in Applied Science and Engineering Technology
سال: 2017
ISSN: 2321-9653
DOI: 10.22214/ijraset.2017.9048