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

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- by A. N. W. Hone PDF
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**359**(2007), 5019-5034 Request permission

## 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.## References

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## Additional Information

**A. N. W. Hone**- Affiliation: Institute of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury CT2 7NF, United Kingdom
- Email: anwh@kent.ac.uk
- Received by editor(s): February 9, 2005
- Received by editor(s) in revised form: September 15, 2005
- Published electronically: April 24, 2007
- © Copyright 2007 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**359**(2007), 5019-5034 - MSC (2000): Primary 11B37, 33E05; Secondary 37J35
- DOI: https://doi.org/10.1090/S0002-9947-07-04215-8
- MathSciNet review: 2320658