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
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.
Somos sequences, elliptic functions, addition theorems.
PDF file (483 kB)
MSC: Primary 11B37; Secondary 33E05
A. A. Illarionov, “On the Somos-4 sequence”, Dal'nevost. Mat. Zh., 18:2 (2018), 183–188
Citation in format AMSBIB
\paper On the Somos-4 sequence
\jour Dal'nevost. Mat. Zh.
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