Semi-classical Laguerre polynomials and a third order discrete integrable equation

Details Semi-classical Laguerre polynomials and a third order discrete integrable equation Semi-classical Laguerre polynomials and a third order discrete integrable equation

2009-07-13

arxiv.org/abs/0907.2158v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

11 pages

Scientific paper

10.1088/1751-8113/42/45/454019

A semi-discrete Lax pair formed from the differential system and recurrence
relation for semi-classical orthogonal polynomials, leads to a discrete
integrable equation for a specific semi-classical orthogonal polynomial weight.
The main example we use is a semi-classical Laguerre weight to derive a third
order difference equation with a corresponding Lax pair.

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