Rational interpolation to solutions of Riccati difference equations on elliptic lattices

Magnus, Alphonse
(2009) 9th Conference on Orthogonal Polynomials, Special Functions and Applications — Location: Marseille(France) (2.July.2007)

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  • Magnus, AlphonseUCLouvain
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Abstract
It is shown how to define difference equations on particular lattices {x(n)}, n is an element of Z, where the x(n)s are values of an elliptic function at a sequence of arguments in arithmetic progression (elliptic lattice). Solutions to special difference equations (elliptic Riccati equations) have remarkable simple (!) interpolatory continued fraction expansions. (C) 2009 Elsevier B.V. All rights reserved.
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Magnus, A. (2009). Rational interpolation to solutions of Riccati difference equations on elliptic lattices. Journal of Computational and Applied Mathematics, 233(3), 793-801. https://doi.org/10.1016/j.cam.2009.02.047 (Original work published 2009)