Minimal recurrence relations for connection coefficients between classical orthogonal polynomials: Continuous case

Connection Coefficients of Orthogonal Polynomials with Applications to Classical Orthogonal Polynomials

New criteria for nonnegativity of connection coefficients between to systems of orthogonal polynomials are given. The results apply to classical orthogonal polynomials.

Connection coefficients for Laguerre–Sobolev orthogonal polynomials

Laguerre–Sobolev polynomials are orthogonal with respect to an inner product of the form 〈p,q〉S = ∫∞ 0 p(x)q(x)x αe−x dx + λ∫∞ 0 p′(x)q′(x)dμ(x), where α > −1, λ 0, and p,q ∈ P, the linear space of polynomials with real coefficients. If dμ(x) = xαe−x dx, the corresponding sequence of monic orthogonal polynomials {Q n (x)} has been studied by Marcellán et al. (J. Comput. Appl. Math. 71 (1996) 24...

Asymptotics of Orthogonal Polynomials via Recurrence Relations

Computation of connection coefficients and measure modifications for orthogonal polynomials

We observe that polynomial measure modifications for families of univariate orthogonal polynomials imply sparse connection coefficient relations. We therefore propose connecting L2 expansion coefficients between a polynomial family and a modified family by a sparse transformation. Accuracy and conditioning of the connection and its inverse are explored. The connection and recurrence coefficient...

A formula for the coefficients of orthogonal polynomials from the three-term recurrence relations

In this work, the coefficients of orthogonal polynomials are obtained in closed form. Our formula works for all classes of orthogonal polynomials whose recurrence relation can be put in the form Rn(x) = x Rn−1(x) − αn−2 Rn−2(x). We show that Chebyshev, Hermite and Laguerre polynomials are all members of the class of orthogonal polynomials with recurrence relations of this form. Our formula unif...