Results 1 to 10 of about 255 (102)
A Family of Theta-Function Identities Based upon Combinatorial Partition Identities Related to Jacobi’s Triple-Product Identity [PDF]
Mathematics, 2020 The authors establish a set of six new theta-function identities involving multivariable R-functions which are based upon a number of q-product identities and Jacobi’s celebrated triple-product identity. These theta-function identities depict the inter-relationships that exist among theta-function identities and combinatorial partition-theoretic ...
Rekha Srivastava +2 more
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New polynomial analogues of Jacobi's triple product and Lebesgue's identities
Advances in Applied Mathematics, 2004 In a recent paper by the authors, a bounded version of Goellnitz's (big) partition theorem was established. Here we show among other things how this theorem leads to nontrivial new polynomial analogues of certain fundamental identities of Jacobi and Lebesgue. We also derive a two parameter extension of Jacobi's famous triple product identity.
Alexander Berkovich +1 more
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The Number-Theoretic Content of the Jacobi Triple Product Identity [PDF]
, 2001 The author presents a new proof of the Jacobi triple product identity, based on its equivalence with an esoteric summation theorem in elementary number theory.
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Partition results related to a special case of Jacobi’s triple product identity
Ramanujan JournalAbstract In this paper some partition results related to a special case of Jacobi’s Triple Product Identity will be presented. These results will be presented both algebraically and combinatorially.
Louis Kolitsch
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A Vanishing Finite Sum associated with Jacobi's triple product identity
Journal of Combinatorial Theory, 1969 AbstractJacobi's triple product identity is shown to be equivalent to the vanishing of a finite sum. The vanishing of the sum is then established independently of Jacobi's identity, and the behavior of a related finite sum is discussed. Finally, the possibility of generalizing Jacobi's identity to include variables with non-quadratic exponents is ...
Kenneth B Stolarsky
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Recurrence relations connecting mock theta functions and restricted partition functions [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 In this paper, we provide some recurrence relations connecting restricted partition functions and mock theta functions. Elementary manipulations are used including Jacobi triple product identity, Euler's pentagonal number theorem, and Ramanujan's theta ...
M. Rana, H. Kaur, K. Garg
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Consequences of a sextuple-product identity
International Journal of Mathematics and Mathematical Sciences, 1987 A sextuple-product identity, which essentially results from squaring the classical Gauss-Jacobi triple-product identity, is used to derive two trigonometrical identities. Several special cases of these identities are then presented and discussed.
John A. Ewell
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Touchard-Riordan formulas, T-fractions, and Jacobi's triple product identity [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 We give a combinatorial proof of a Touchard-Riordan-like formula discovered by the first author. As a consequence we find a connection between his formula and Jacobi's triple product identity. We then give a combinatorial analog of Jacobi's triple product identity by showing that a finite sum can be interpreted as a generating function of weighted ...
Josuat-Vergès, Matthieu, Kim, Jang Soo
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On relationships between q-products identities, Ralpha, Rbeta and Rm functions related to Jacobi's triple-product identity [PDF]
Mathematica Moravica, 2020 The authors establish a set of two new relationships involving q-product identities, Ralpha, Rbeta, and Rm (m = 1, 2, 3, . . .) functions; and answer a open question of Srivastava et al. [18]. The present work is motivated and based upon recent findings of Chaudhary et al. [8].
Chaudhary M.P., Chaudhary Sangeeta
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Triple product identities for the Jacobi symbol
Expositiones Mathematicae, 2001 Choose three \(2\times 2\) matrices \(A_j=\left(\begin{matrix} a_j & b_j\\ c_j & d_j\end{matrix}\right)\) with integer entries having \(c_j\) odd and positive such that \(A_1A_2A_3=-I\). The author shows that the product of the Jacobi symbols \(\prod^3_{j=1} \left(\frac{a_j}{c_j}\right)\) is \((-1)\) to the power \(\frac 14\sum_ ...
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