Clarkson, Peter A.Jordaan, Kerstin HeidrunKelil, Abey2016-07-132016-04Clarkson, PA, Jordaan, K, & Kelil, A 2016, 'A generalized Freud weight', Studies in Applied Mathematics, vol. 136, no. 6, pp. 288-320.0022-2526 (print)1467-9590 (online)10.1111/sapm.12105http://hdl.handle.net/2263/55754We discuss the relationship between the recurrence coefficients of orthogonal polynomials with respect to a generalized Freud weight w(x; t ) = |x|2λ+1 exp(−x4 + tx2), x ∈ R, with parameters λ > −1 and t ∈ R, and classical solutions of the fourth Painlev´e equation. We show that the coefficients in these recurrence relations can be expressed in terms of Wronskians of parabolic cylinder functions that arise in the description of special function solutions of the fourth Painlev´e equation. Further we derive a second-order linear ordinary differential equation and a differential-difference equation satisfied by the generalized Freud polynomials.en© 2015 Wiley Periodicals, Inc. This is the pre-peer reviewed version of the following article : A generalized Freud weight, Studies in Applied Mathematics, vol. 136, no. 6, pp. 288-320, 2016. doi :10.1111/sapm.12105, which has been published in final form at : http://onlinelibrary.wiley.com/journal/10.1111/(ISSN)1467-9590.Freud weightRecurrence coefficientsRelationshipOrthogonal polynomialsPostprint Article