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Finite form of the quintuple product identity

WebTriple product, quintuple product, linear identity, search algorithm. ... is a Laurent series with a finite number of negative-degree terms, which is a power series iff 1 E [-k, k]. ... We say that T2+,E(k, 1) is in reduced form whenever 0 < 1 < k. The next two formulas allow us to put any T2a+3E(k, 1) into reduced form (cf. [4, ... WebNov 1, 2024 · The quintuple product identity (1.1) or its equivalent forms were discovered by Fricke [3], Ramanujan [5] and Watson [6]. This identity has important applications in …

A new semi-finite form of the quintuple product identity

WebMar 1, 1993 · Durfee rectangles and the Jacobi triple product identity. C. Wenchang. Published 1 March 1993. Mathematics. Acta Mathematica Sinica. By means of the Durfee rectangles of partitions, a very elementary proof for Jacobi's triple product identity and its finite analogue is presented. View on Springer. WebFinite form of the quintuple product identity @article{Chen2006FiniteFO, title={Finite form of the quintuple product identity}, author={William Y. C. Chen and Wenchang Chu and Nancy S. S. Gu}, journal={J. Comb. Theory, Ser. go fishing auf facebook https://luney.net

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WebIn mathematics the Watson quintuple product identity is an infinite product identity introduced by Watson and rediscovered by Bailey (1951 ) and ... W., & Gu, N. S. (2005). … WebCiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Recently, Chen-Chu-Gu [4] and Guo-Zeng [6] found independently that Watson’s quintuple … WebAug 9, 2024 · The quintuple product identity can be read, and used, in two quite different ways. It gives us the series expansion of the left side, but it also shows how in some circumstances two triple products can be summed to a single product . In § 10.2, I will present as direct a proof as I can, while in § 10.3, I will present a generalisation, which ... go fishing app

A semi-finite form of the quintuple product identity

Category:THE QUINTUPLE PRODUCT IDENTITY International Journal of …

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Finite form of the quintuple product identity

Sum to Product Identities SpringerLink

WebThe celebrated quintuple product identity follows surprisingly from an almost-trivial algebraic identity, which is the limiting case of the terminating q-Dixon formula. … WebFinite form of the quintuple product identity WilliamY.C. Chen,Wenchang Chu, Nancy S.S. Gu Center for Combinatorics, LPMC, Nankai University, Tianjin 300071, PR China Received 25 February 2005 Communicated by GeorgeAndrews Available online 26 May 2005 Abstract The celebrated quintuple product identity follows surprisingly from an …

Finite form of the quintuple product identity

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WebThe simplest proof of Jacobi's triple product identity originally due to Cauchy (1843) and Gauss (1866) is reviewed. In the same spirit, we prove by means of induction principle and finite difference method, a finite form of the quintuple product identity. WebFinite form of the quintuple product identity Computing methodologies Symbolic and algebraic manipulation Symbolic and algebraic algorithms Algebraic algorithms Mathematics of computing Discrete mathematics Combinatorics Mathematical analysis Numerical analysis Computations in finite fields Comments

WebMay 13, 2005 · In addition, Paule [28] found a finite form of the quintuple product identity. Two further finite forms have been given in the recent papers [7] and ... WebMar 24, 2024 · The quintuple product identity, also called the Watson quintuple product identity, states (1) It can also be written (2) or (3) The quintuple product identity can …

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WebMay 1, 2024 · Abstract. Recently, the authors (Zhu and Zhang, 2024) [9] derived a semi-finite form of the quintuple product identity. In this note, further two semi-finite forms …

WebJul 24, 2024 · The quintuple product identity are deduced from a new semi-finite form, which are obtained from the very-well-poised series. Comments: 3 pages. Subjects: Combinatorics (math.CO) MSC classes: 33D15, 11F27. Cite as: go fishin gameWebAug 9, 2024 · The quintuple product identity can be read, and used, in two quite different ways. It gives us the series expansion of the left side, but it also shows how in some … go fishing 2WebCiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Recently, Chen-Chu-Gu [4] and Guo-Zeng [6] found independently that Watson’s quintuple product identity follows surprisingly from two basic algebraic identities, called finite forms of Watson’s quintuple product identity. The present paper shows that both identities are … go fishing by the lakeWebA NEW SEMI-FINITE FORM OF THE QUINTUPLE PRODUCT IDENTITY JUN-MING ZHU Abstract. The quintuple product identity are deduced from a new semi-finite form, which are obtained from the very-well-poised 6φ 5 series. 1. Introduction Throughout this paper the product of q-shifted factorials are defined by (a;q)∞ = Y∞ l=0 (1 −aql) and (a;q) n ... go fishing canadaWebThe celebrated quintuple product identity follows surprisingly from an almost-trivial algebraic identity, which is the limiting case of the terminating q-Dixon formula. Finite form of the … go fishing by the riverWebJul 24, 2024 · The quintuple product identity are deduced from a new semi-finite form, which are obtained from the very-well-poised series. Comments: 3 pages. Subjects: … go fishing carnival gamehttp://www.billchen.org/publications.html go fishing book