A. A. Illarionov, “On the Somos-4 sequence”, Dal'nevost. Mat. Zh., 18:2 (2018), 183

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Dal'nevostochnyi Matematicheskii Zhurnal, 2018, Volume 18, Number 2, Pages 183–188 (Mi dvmg379)

This article is cited in 3 scientific papers (total in 3 papers)

On the Somos-4 sequence

A. A. Illarionov^ab

^a Khabarovsk Division of the Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences
^b Pacific National University, Khabarovsk

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Abstract: In 2005 A.N.W. Hone has obtained an explicit formula for Somos-4 sequences in terms of the Weierstrass sigma function. The proof is valid only for sequences without zero terms. We prove that arbitrary sequence satisfying the Somos-4 equation is determined by the same formula iff it satisfies some determinant identity (analogue of the formula of addition). We give examples of sequences that satisfy the Somos-4 equation but do not satisfy the determinant identity.

Key words: Somos sequences, elliptic functions, addition theorems.

Funding agency	Grant number
Russian Foundation for Basic Research	18-01-00638

Received: 16.10.2018

Document Type: Article

UDC: 517.52+512.742.72

MSC: Primary 11B37; Secondary 33E05

Language: Russian

Citation: A. A. Illarionov, “On the Somos-4 sequence”, Dal'nevost. Mat. Zh., 18:2 (2018), 183–188

Citation in format AMSBIB

\Bibitem{Ill18}

\by A.~A.~Illarionov

\paper On the Somos-4 sequence

\jour Dal'nevost. Mat. Zh.

\yr 2018

\vol 18

\issue 2

\pages 183--188

\mathnet{http://mi.mathnet.ru/dvmg379}

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https://www.mathnet.ru/eng/dvmg/v18/i2/p183

This publication is cited in the following 3 articles:

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References:	43

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