FoCM 2014 conference

Workshop C5 - Special Functions and Orthogonal Polynomials

No date set

The relationship between the fifth Painlev\'e equation and orthogonal polynomials

Peter Clarkson

University of Kent, United Kingdom   -

Here we are concerned with orthogonal polynomials for a deformed Laguerre weight. It is shown that the coefficients of the three-term recurrence relation satisfied by the polynomials can be expressed in terms of Wronskians which involve Kummer functions. These Wronskians are related to special function solutions of the fifth Painlev\'e equation. Using this relationship we can explicitly write the recurrence relation coefficients in terms of exact solutions of the fifth Painlev\'e equation.

Joint work with J Smith (University of Kent, UK).

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