Rational Solutions for the Discrete Painlevé II Equation

Details Rational Solutions for the Discrete Painlevé II Equation Rational Solutions for the Discrete Painlevé II Equation

1997-02-10

arxiv.org/abs/solv-int/9702001v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

12 pages, latex

Scientific paper

10.1016/S0375-9601(97)00397-6

The rational solutions for the discrete Painlev\'e II equation are
constructed based on the bilinear formalism. It is shown that they are
expressed by the determinant whose entries are given by the Laguerre
polynomials. Continuous limit to the Devisme polynomial representation of the
rational solutions for the Painlev\'e II equation is also discussed.

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