Results 1 to 10 of about 1,982 (184)
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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Some new relations between T(a₁,a₂,a₃,a₄,a₅; n) and N(a₁,a₂,a₃,a₄,a₅; n) [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 Let N(a₁,a₂,a₃,a₄,a₅; n) and T(a₁,a₂,a₃,a₄,a₅; n) count the representations of n as a₁x₁²+a₂x₂²+a₃x₃²+a₄x₄²+a₅x₅² and a₁X₁(X₁+1)/2+a₂X₂(X₂+1)/2+a₃X₃(X₃+1)/2+a₄X₄(X₄+1)/2+a₅X₅(X₅+1)/2, respectively, where a₁,a₂,a₃,a₄,a₅ are positive integers, x₁,x₂,x₃,x₄ ...
Vandna, Mandeep Kaur
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Partition-theoretic interpretations of some q-series identities of Ramanujan
Kuwait Journal of Science, 2021 Ramanujan's lost notebook contains several $q$-series identities and some of them have theta-function representations. We give partition-theoretic interpretations of some of these identities and prove Ramanujan-type congruences for certain partition ...
Nipen Saikia
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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 Special Integer Partitions Generated by a Family of Functions
Trends in Computational and Applied Mathematics, 2023 In this work, inspired by Ramanujan’s fifth order Mock Theta function f1(q), we define a collection of functions and look at them as generating functions for partitions of some integer n containing at least m parts equal to each one of the numbers from
M. L. Matte
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Theta function identities involving fourth power [PDF]
Notes on Number Theory and Discrete MathematicsOn page 241 of his Second Notebook, Ramanujan recorded one of his theta function identity, which involves the ratio of the fourth power of theta functions with respect to ψ(q). In this article, we give a new proof for this theta function identity.
Praveenkumar, Siddaraju, R. Rangarajan
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Some Ramanujan-type circular summation formulas
Advances in Difference Equations, 2020 In this paper, we give two Ramanujan-type circular summation formulas by applying the way of elliptic functions and the properties of theta functions.
Ji-Ke Ge, Qiu-Ming Luo
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Applications of an identity of Andrews
Arab Journal of Mathematical Sciences, 2014 In this paper, we give a bilateral form of an identity of Andrews, which is a generalization of the 1ψ1 summation formula of Ramanujan. Using Andrews’ identity, we deduce some new identities involving mock theta functions of second order and finally, we ...
D.D. Somashekara, K. Narasimha Murthy
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Theta function identities from optical neural network transformations
International Journal of Mathematics and Mathematical Sciences, 1993 We take a new approach to the generation of Jacobi theta function identities. It is complementary to the procedure which makes use of the evaluation of Parseval-like identities for elementary cylindrically-symmetric functions on computer holograms.
E. Elizalde, A. Romeo
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Journal of Applied Mathematics, 2013 By employing Hirota bilinear method, we mainly discuss the (3+1)-dimensional potential-YTSF equation and discrete KP equation. For the former, we use the linear superposition principle to get its N exponential wave solutions.
Yan Wang, Zhenhui Wang
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