Results 11 to 20 of about 4,592,487 (264)
On two theta function identities of Ramanujan [PDF]
Indian Journal of Pure and Applied Mathematics, 2022 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
K. R. Vasuki, A. I. Vijaya Shankar
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Theta function identities and q series [PDF]
, 2023 We establish some functional identities of theta functions, an elementary proof of classical fourth-order identities, Landen transformations, and q series from the eigenvectors of the discrete Fourier transform. Also, we derive connection between Rogers-Ramanujan type identity and theta function identity.
Masal, Hemant +2 more
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Theta-function identities and the explicit formulas for theta-function and their applications [PDF]
Journal of Mathematical Analysis and Applications, 2004 Let \(h_{k,n}= \frac{\varphi(e^{-\pi\sqrt{n/k}})} {k^{1/4}\varphi(e^{-\pi\sqrt{nk}})}\) and \(h_{k,n}'= \frac{\varphi(-e^{-2\pi\sqrt{n/k}})} {k^{1/4}\varphi(-e^{-2\pi\sqrt{nk}})},\) where \(\varphi(q)=\sum_{j=-\infty}^\infty q^{j^2}\). Properties of \(h_{k,n}\) and \(h_{k,n}'\) are studied, and \(h_{k,n}\) and \(h_{k,n}'\) are explicitly evaluated for ...
Yi, Jinhee
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Theta function identities and Ramanujan's Congruences on the partition function
The Quarterly Journal of Mathematics, 2005 A q-difference equation on eight shifted factorials of infinite order will be established. As consequences, we shall systematically explore triple products to give alternative proofs of the theta function identities due to Ewell [5, 6] and Berndt et al. [2] and briefly review their applications to the Ramanujan congruences on the partition function. In
CHU, Wenchang
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On series identities arising from Jacobi’s identity of the theta function
International Journal of Number Theory, 2018 In this paper, we show certain series identities arising from the Jacobi identity of the ordinary theta function. These include several formulas of Ramanujan type given by Berndt and their relevant analogues.
Hirofumi Tsumura
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Jacobi's triple product identity and theta function identities [PDF]
Mathematical Communications, 2011 As a unified approach, Jacobi's triple product identity will be utilized to derive theta function formulae due to Baruah-Berndt (2007), identities of Rogers--Ramanujan functions and modular equations due to Ramanujan.
Chu, Wenchang, Yan, Qinglun
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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 also considered.
M.P. Chaudhary +2 more
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On generalization of a Ramanujan’s theta function identity
Boletín de la Sociedad Matemática Mexicana, 2022 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Nanjundegowda, Harshitha, K.
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On certain identities in theta functions [PDF]
Transactions of the American Mathematical Society, 1930 1. The purpose of this paper is to obtain certain identities in Jacobi's theta functions by a new method. This method may be outlined as follows. We consider two sets of elements S and Si, conceptually distinct, such that the elements of S are in one-to-one correspondence with the elements of S1.
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Ramanujan Theta Function Identities and Quadratic Numbers [PDF]
, 2023 Eigenvectors of the discrete Fourier transform can be expressed using Ramanujan theta functions. New theta function identities, Ramanujan theta function identities, and generating functions for the quadratic numbers are a consequence.Comment: 11 ...
Kendre, Subhash +2 more
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