Far Eastern Mathematical Journal

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On the Somos-4 sequence


Illarionov A.A.

2018, issue 2, Ñ. 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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