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A cubic counterpart of Jacobi's identity and the AGM
We produce exact cubic analogues of Jacobi's celebrated theta function identity and of the arithmetic-geometric mean iteration of Gauss and Legendre. The iteration in question is an+1 := an + 2bn / 3 and bn+1 := [formula cannot be replicated].
J. M. Borwein (21268130) +1 more
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Friedrich Heinrich Jacobi's Werke
FRIEDRICH HEINRICH JACOBI'S WERKE Friedrich Heinrich Jacobi's Werke J. G. Hamann's Briefwechsel mit F. H. Jacobi (4,3.1819) ( -
Jacobi, Friedrich Heinrich
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Friedrich Heinrich Jacobi's auserlesener Briefwechsel
FRIEDRICH HEINRICH JACOBI'S AUSERLESENER BRIEFWECHSEL Friedrich Heinrich Jacobi's auserlesener Briefwechsel [...] (Bd. 1) ( -
Roth, Karl Johann Friedrich von +1 more
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Signature title: Jacobi's Werke. VIII. Bd. Issued as last vol. of the collected ed.
Ittner, Joseph Albert von 1754-1825.
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Proceeding of 10th Triple Helix International Conference 2012
, 2013 Triple Helix International Conference
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Gaussian sums, Dedekind sums and the Jacobi triple product identity
Gaussian sums, Dedekind sums and the Jacobi triple product identityopenaire +1 more source
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Two generalizations of Jacobi’s triple product identity and their applications
The Ramanujan Journal, 2022There are two main theorems in the paper under review and they are exactly two generalizations of Jacobi's triple product identity. The proofs are based on the Andrews' series rearrangement method. As applications, the authors use their formulae for mock theta functions and Rogers-Ramanujan identities.
Chuanan Wei, Yuanbo Yu, Qiuxia Hu
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Jacobi's Triple-Product Identity and an Associated Family of Theta-Function Identities
Математические заметки, 2022The main object of this paper is to present a family of $q$-series identities which involve some of the theta functions of Jacobi and Ramanujan. Each of these (presumably new) $q$-series identities reveals interesting relationships among three of the theta-type functions which stem from the celebrated Jacobi's triple-product identity in a remarkably ...
Srivastava, H. M. +3 more
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A combinatorial proof of Jacobi’s triple product identity
The Ramanujan Journal, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Louis W. Kolitsch, Stephanie Kolitsch
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