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SOME INVERSE RELATIONS AND THETA FUNCTION IDENTITIES
International Journal of Number Theory, 2012Two pairs of inverse relations for elliptic theta functions are established with the method of Fourier series expansion, which allow us to recover many classical results in theta functions. Many nontrivial new theta function identities are discovered. Some curious trigonometric identities are derived.
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Several identities for certain products of theta functions
The Ramanujan Journal, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A Family of Theta-Function Identities Related to Jacobi’s Triple-Product Identity
Russian Journal of Mathematical Physics, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Srivastava, H. M. +2 more
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A theta function identity and its applications
The Ramanujan Journal, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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An Identity Relating a Theta Function to a Sum of Lambert Series
Bulletin of the London Mathematical Society, 2001Summary: 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. +2 more
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FOUR IDENTITIES FOR THIRD ORDER MOCK THETA FUNCTIONS
Nagoya Mathematical Journal, 2018In 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. +4 more
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On the Andrews–Yee Identities Associated with Mock Theta Functions
Annals of Combinatorics, 2019In 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, 1999Let \(S_n\) 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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Identities for Ramanujan's Sixth-Order Mock Theta Functions
The Quarterly Journal of Mathematics, 2002Six 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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Far East Journal of Mathematical Sciences (FJMS), 2017
Mahendra Pal Chaudhary +2 more
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Mahendra Pal Chaudhary +2 more
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