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arXiv · 0907.2158

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

P. E. Spicer·F. W. Nijhoff
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Abstract

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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P. E. Spicer, F. W. Nijhoff. 2009-07-13. Semi-classical Laguerre polynomials and a third order discrete integrable equation. https://doi.org/10.1088/1751-8113%2F42%2F45%2F454019

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