Sigma function solution of the initial value problem for Somos 5 sequences
By Andrew N. W. Hone. 2005
64 citations recorded by the source corpus.
The Somos 5 sequences are a family of sequences defined by a fifth order bilinear recurrence relation with constant coefficients. For particular choices of coefficients and initial data, integer sequences arise. By making the connection with a second order nonlinear mapping with a first integral, we prove that the two subsequences of odd/even index terms each satisfy a Somos 4 (fourth order) recurrence. This leads directly to the explicit solution of the initial value problem for the Somos 5 sequences in terms of the Weierstrass sigma function for an associated elliptic curve.
Subfields: Computational Mathematics, Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/bd979e7e501812614ca6288877c8f01a89b145e7
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In Computational Mathematics
In Computational Theory and Mathematics
In Geometry and Topology
Citations in the corpus
- Introduction to Cluster Algebras (2018, background): “Some of the many other systems that have been investigated from a cluster algebra point of view are Q-systems [9], T -systems [8], Somos sequences [31], and mutations in box products of quivers [44].”