The relationship between semi-classical Laguerre polynomials and the fourth Painlevé equation
نویسندگان
چکیده
We discuss the relationship between the recurrence coefficients of orthogonal polynomials with respect to a semiclassical Laguerre weight and classical solutions of the fourth Painlevé equation. We show that the coefficients in these recurrence relations can be expressed in terms of Wronskians of parabolic cylinder functions which arise in the description of special function solutions of the fourth Painlevé equation.
منابع مشابه
Semi-classical Laguerre polynomials and a third order discrete integrable equation
The connection between semi-classical orthogonal polynomials and discrete integrable systems is well established. The earliest example of a discrete integrable system in semi-classical orthogonal polynomials can be attributed first to Shohat in 1939 [16], then second by Freud [10] in 1976. However it wasn’t until the 1990’s, when the focus within integrable systems shifted from continuous to di...
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