FAR EASTERN BRANCH OF THE RUSSIAN ACADEMY OF SCIENCES
INSTITUTE OF APPLIED MATHEMATICS KHABAROVSK DIVISION
Far Eastern Mathematical Journal
On the Somos-4 sequence |
Illarionov A.A. |
2018, issue 2, P. 183-188 |
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. |
Keywords: Somos sequences, elliptic functions, addition theorems |
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References |
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