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A cubic counterpart of Jacobi's identity and the AGM

Borwein, Jonathan M. and Borwein, Peter (1991) A cubic counterpart of Jacobi's identity and the AGM. Trans. Amer. Math. Soc., 323 . pp. 691-701.

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    Abstract

    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 $a_n+1 := a_n + 2b_n / 3$ and b_n+1 := [formula cannot be replicated]. The limit of this iteration is identified in terms of the hypergeometric function ₂F₁ (1/3, 2/3; 1 ; ·), which supports a particularly simple cubic transformation.

    Item Type: Article
    Subjects: UNSPECIFIED
    Faculty: UNSPECIFIED
    Depositing User: Mrs Naghmana Tehseen
    Date Deposited: 18 Feb 2015 14:51
    Last Modified: 18 Feb 2015 14:51
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/1578

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