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Dal'nevost. Mat. Zh., 2018, Volume 18, Number 2, Pages 183–188 (Mi dvmg379)  

On the Somos-4 sequence

A. A. Illarionovab

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

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


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Document Type: Article
UDC: 517.52+512.742.72
MSC: Primary 11B37; Secondary 33E05
Received: 16.10.2018

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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