A family of second degree semi-classical forms of class s=1

Abstract

Let u(β 0 ) be the regular form fulfilling (u(β 0 )) 2n+1 = β 0 (u(β 0 )) 2n , n ≥ 0 where β 0 is an arbitrary complex number in such a way that for β 0 = 0 one has the symmetric forms. Recently, the second degree symmetric semi-classical forms (when β 0 = 0) of class s ≤ 1 were determined. In this paper, we determine all the semi-classical forms u(β 0 ) of class s = 1, which are also of second degree when β 0 = 0.

Some Laguerre-Hahn Orthogonal Polynomials of Class One

“…gives H(1) = D 0 (1) = 0, since u is a Laguerre-Hahn form of class s u = 1 and it satisfies (14). Hence, equation (21…”

“…Thus Ψ(1) = B (1) = 0 which contradiction (Ψ(1), B (1)) = (0, 0). Necessarily (2b 3 −c 2 −3, b 3 +b 1 ) = (0, 0).Moreover the form u is of class one, we shall have the condition(14) with Z Φ = {−1, 0, 1}, which leads to relation (26).…”

Orthogonality of the Dickson polynomials of the $(k+1)$-th kind

“…Stieltjes transforms satisfying quadratic equations with polynomial coefficients are called second degree forms; see [2], [6], [45], and [49].…”

Orthogonality of the Dickson polynomials of the (k+1)-th kind

“…Stieltjes transforms satisfying quadratic equations with polynomial coefficients are called second degree forms. See [2], [6], [43], and [48].…”