A generalized sextic Freud weight

We discuss the recurrence coefficients of orthogonal polynomials with respect to a generalised sextic Freud weight ω(x;t, λ) = |x|\(^{2λ+1}\), x ∈ R, with parameters λ > −1 and t ∈ R. We show that the coefficients in these recurrence relations can be expressed in terms of Wronskians of generalised hypergeometric functions 1F2(a1; b1, b2; z). We derive a nonlinear discrete as well as a system of differential equations satisfied by the recurrence coefficients and use these to investigate their asymptotic behaviour. We conclude by highlighting a fascinating connection between generalised quartic, sextic, octic and decic Freud weights when expressing their first moments in terms of generalised hypergeometric functions.