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.
Hari Mohan Srivastava +3 more
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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.
Matthieu Josuat-Vergès, Jang-Soo Kim
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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].
Chaudhary M.P., Chaudhary Sangeeta
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Some identities associated with theta functions and tenth order mock theta functions [PDF]
Mathematica MoravicaThe main objective of this paper is to present some identities associated with theta functions and tenth order mock theta functions. Several closely-related identities such as (for example) q-product identities and Jacobi's triple-product identity are ...
Chaudhary M.P. +2 more
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On relationships between q-product identities and combinatorial partition identities [PDF]
Mathematica Moravica, 2020 Andrews et al. [2] discussed about the combinatorial partition identities. We aim to present some relationships between q-product identities and combinatorial partition identities, by using and combining known formulas.
Chaudhary M.P. +2 more
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A Note on Four-Variable Reciprocity Theorem
International Journal of Mathematics and Mathematical Sciences, 2009 We give new proof of a four-variable reciprocity theorem using Heine's transformation, Watson's transformation, and Ramanujan's 1𝜓1-summation formula. We also obtain a generalization of Jacobi's triple product identity.
Chandrashekar Adiga, P. S. Guruprasad
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Several identities in statistical mechanics
International Journal of Mathematics and Mathematical Sciences, 1994 In an earlier paper concerning a solvable Inodel in statistical mechanics, Miwa and Jimbo state a theta-function identity which they have checked to the 200th power, but of which they do not have a proof.
M. D. Hirschhorn
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Kostant partition functions for affine Kac-Moody algebras
International Journal of Mathematics and Mathematical Sciences, 1997 Employing the method of generating functions in conjunction with various number-thoretic identities, we obtain recursion relations for the Kostant partition functions for the affine Kac-Moody algebras The partition functions for the higher rank algebras ...
T. S. Santhanam, R. Chakrabarti
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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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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.
Department of Mathematics, The University of Florida, Gainesville, FL 32611, USA ( host institution ) +2 more
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