Two-parameter Turan inequalities for ultraspherical and Laguerre polynomials

Jensen Polynomials and the Turan and Laguerre Inequalities

Ultraspherical Type Generating Functions for Orthogonal Polynomials

We characterize the probability distributions of finite all order moments having generating functions for orthogonal polynomials of ultraspherical type. 1. Motivation: Meixner families There is a one to one correspondance between probability distributions on the real line and polynomials of a one variable satisfying a three-terms recurrence relation subject to some positive conditions ([9]). Th...

Ultraspherical Type Generating Functions for Orthogonal Polynomials

We characterize, up to a conjecture, probability distributions of finite all order moments with ultraspherical type generating functions for orthogonal polynomials. 1. Motivation: Meixner families There is a one to one correspondance between probability distributions on the real line and polynomials of a one variable satisfying a three-terms recurrence relation subject to some positivity condit...

Ultraspherical Type Generating Functions for Orthogonal Polynomials

We characterize, under some technical assumptions and up to a conjecture, probability distributions of finite all order moments with ultraspherical type generating functions for orthogonal polynomials. Our method is based on differential equations and the obtained measures are particular Beta distributions. We actually recover the free Meixner family of probability distributions so that our met...

Differential Equations for Symmetric Generalized Ultraspherical Polynomials

We look for differential equations satisfied by the generalized Jacobi polynomials { P n (x) }∞ n=0 which are orthogonal on the interval [−1, 1] with respect to the weight function Γ(α+ β + 2) 2α+β+1Γ(α+ 1)Γ(β + 1) (1− x)(1 + x) +Mδ(x+ 1) +Nδ(x− 1), where α > −1, β > −1, M ≥ 0 and N ≥ 0. In the special case that β = α and N = M we find all differential equations of the form ∞ ∑ i=0 ci(x)y (x) =...