## Sigma function solution of the initial value problem for Somos 5 sequences (2008)

by
A. N. W. Hone

Citations: | 6 - 4 self |

### BibTeX

@MISC{Hone08sigmafunction,

author = {A. N. W. Hone},

title = {Sigma function solution of the initial value problem for Somos 5 sequences},

year = {2008}

}

### OpenURL

### Abstract

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.