Results 201 to 210 of about 2,032 (227)

Several identities for certain products of theta functions

The Ramanujan Journal, 2008
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A Family of Theta-Function Identities Related to Jacobi’s Triple-Product Identity

Russian Journal of Mathematical Physics, 2020
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Srivastava, H. M., Chaudhary, M. P., Chaudhary, S.   +2 more
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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.
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A theta function identity and its applications

The Ramanujan Journal, 2014
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An Identity Relating a Theta Function to a Sum of Lambert Series

Bulletin of the London Mathematical Society, 2001
Summary: We derive an identity connecting a theta function and a sum of Lambert series. As a consequence of this identity, we deduce a number of results of Jacobi, Dirichlet, Lorenz, Ramanujan and Rademacher.
Andrews, George E., Lewis, Richard, Liu, Zhi-Guo   +2 more
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FOUR IDENTITIES FOR THIRD ORDER MOCK THETA FUNCTIONS

Nagoya Mathematical Journal, 2018
In 2005, using a famous lemma of Atkin and Swinnerton-Dyer (Some properties of partitions, Proc. Lond. Math. Soc. (3)4(1954), 84–106), Yesilyurt (Four identities related to third order mock theta functions in Ramanujan’s lost notebook, Adv. Math. 190(2005), 278–299) proved four identities for third order mock theta functions found on pages 2 and 17 in ...
Andrews, George E., Berndt, Bruce C., Chan, Song Heng, Kim, Sun, Malik, Amita   +4 more
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On the Andrews–Yee Identities Associated with Mock Theta Functions

Annals of Combinatorics, 2019
In the paper under review, the authors generalize the Andrews-Yee identities associated with the third-order mock theta functions \(\omega(q)\) and \(\nu(q)\). They obtain some \(q\)-series transformation formulas, one of which gives a new Bailey pair. Using the classical Bailey lemma, they derive a product formula for two \(_2\phi_1\) series.
Wang, Jin, Ma, Xinrong
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Macdonald identities and multidimensional theta-functions

Journal of Mathematical Sciences, 1999
Let \(S_n\) be the symmetric group of order \(n\) and \(\# \sigma\) be the sign of the permutation \(\sigma\in S_n\). When \(\sigma=(p_0\quad p_1\cdots p_{n-1})\), define \(I(\sigma)\) by \[ I(\sigma) :=\{l\in\mathbb Z: l_j\equiv j-p_j\pmod n, j=1,\cdots, n-1\}. \] Set \[ F_n:=F_n(y_1,\cdots, y_{n-1},q):= \sum_{\sigma\in S_n} (-1)^{\# \sigma}\sum_{l\in
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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
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Identities for Ramanujan's Sixth-Order Mock Theta Functions

The Quarterly Journal of Mathematics, 2002
Six identities for sixth-order mock theta functions are proved. One of these was given by Ramanujan in the ``Lost Notebook'' and was subsequently studied by \textit{G. Andrews} and \textit{D. Hickerson} [Adv. Math. 89, No. 1, 60-105 (1991; Zbl 0739.11042)]. The other five identities are new.
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