The basic bilateral hypergeometric series
WebApr 30, 1991 · This article is published in Bulletin of The London Mathematical Society.The article was published on 1991-05-01. It has received 922 citation(s) till now. The article focuses on the topic(s): Basic hypergeometric series. WebNov 24, 2009 · Bilateral basic hypergeometric series. 6. The Askey–Wilson q-beta integral and some associated formulas. 7. Applications to orthogonal polynomials. 8. Further …
The basic bilateral hypergeometric series
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In mathematics, a bilateral hypergeometric series is a series Σan summed over all integers n, and such that the ratio an/an+1 of two terms is a rational function of n. The definition of the generalized hypergeometric series is similar, except that the terms with negative n must vanish; the bilateral series will in … See more The bilateral hypergeometric series pHp is defined by where $${\displaystyle (a)_{n}=a(a+1)(a+2)\cdots (a+n-1)\,}$$ See more • Basic bilateral hypergeometric series See more Suppose that none of the variables a or b are integers, so that all the terms of the series are finite and non-zero. Then the terms with n<0 … See more Dougall's bilateral sum (Dougall 1907) This is sometimes written in the equivalent form See more There are two forms of basic hypergeometric series, the unilateral basic hypergeometric series φ, and the more general bilateral basic hypergeometric series ψ. The unilateral basic hypergeometric series is defined as where and
WebBilateral basic hypergeometric series; Jacobi’s triple product identity; mock theta functions; theta functions. 2010 Mathematics Subject Classification. 33D15. 1. Introduction Euler was the first to introduce the concept of basic hypergeometric series in 1748. But Heine made this into a systematic theory by generalizing Gauss’ 2F1 series. WebJun 4, 2024 · Euler was the first to introduce the concept of basic hypergeometric series in 1748. But Heine made this into a systematic theory by generalizing Gauss’ \(_2F_1\) …
WebOn the 3ψ3 Basic Bilateral Hypergeometric Series Summation Formulas K. R.Vasuki and G.Sharath (Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysore-570 006, INDIA) E-mail: vasuki−[email protected], sharath−gns@rediffmail.com Abstract: H.Exton has recorded two 3ψ3 basic bilateral hypergeometric series summation WebDec 1, 2007 · We can let n → ∞ in the last equation to get the bilateral series identity subjected to suitable convergence of each series. Using this technique, Zhang and Zhang [28] have derived two new ...
WebOct 16, 2000 · In this article we derive some identities for multilateral basic hypergeometric series associated to the root system An. First, we apply Ismail's [15] argument to an An q-binomial theorem of Milne [25, Theorem 5.42] and derive a new A n generalization of Ramanujan's 1 ψ 1 summation theorem. From this new A n 1 ψ 1 summation and from an …
WebMar 30, 1998 · T. H. Baker, P. J. Forrester. We study multivariable (bilateral) basic hypergeometric series associated with (type ) Macdonald polynomials. We derive several transformation and summation properties for such series including analogues of Heine's transformation, the -Pfaff-Kummer and Euler transformations, the -Saalschütz summation … grimsby equal loginhttp://fs.unm.edu/IJMC/OnTheBasicBilateralHypergeometric.pdf grimsby emergency plumbingWebOn a New Summation Formula for 2^2 Basic Bilateral Hypergeometric Series and Its Applications D. D. Somashekara, K. Narasimha Murthy, and S. L. Shalini Department of … grimsby employershttp://open.docin.com/search.do?nkey=NONSYMMETRIC%2B+INTERPOLATION+%2BMACDONALD+POLYNOMIALS+AND+gln+BASIC+HYPERGEOMETRIC+SERIES&searchcat=1001&mode=4&from=end&fnorePage=¤tPage=4 grimsby employment agenciesWebApr 1, 2007 · Abstract.We prove some new semi-finite forms of bilateral basic hypergeometric series. One of them yields in a direct limit Bailey’s celebrated 6ψ6 summation formula, answering a question recently raised by Chen and Fu. fifty first shadesWebOct 4, 2004 · Basic Hypergeometric Series. This revised and expanded new edition will continue to meet the needs for an authoritative, up-to-date, self contained, and … grimsby employmentWebfield of basic hypergeometric series, or q-series. It contains almost all of the important summation and transformation formulas of basic hypergeometric series one needs to know for work in fields such as combinatorics, number theory, modular forms, quan-tum groups and algebras, probability and statistics, coherent-state theory, orthogonal grimsby elephant scene