Asymptotics for Polynomials Satisfying a Certain Twin Asymptotic Periodic Recurrence Relation: Unbounded Cases

Ratio Asymptotics for Orthogonal Matrix Polynomials with Unbounded Recurrence Coefficients

In this work is presented a study on matrix biorthogonal polynomials sequences that satisfy a nonsymmetric recurrence relation with unbounded coefficients. The ratio asymptotic for this family of matrix biorthogonal polynomials is derived in quite general assumptions. It is considered some illustrative examples.

Asymptotics of Orthogonal Polynomials via Recurrence Relations

Orthogonal Polynomials Defined by a Recurrence Relation

R. Askey has conjectured that if a system of orthogonal polynomials is defined by the three term recurrence relation xp„-,(x) = -^ p„(x) + an_xPn_x(x) + -^pn-2(x) In tn-\ and (-0 then the logarithm of the absolutely continuous portion of the corresponding weight function is integrable. The purpose of this paper is to prove R. Askey's conjecture...

Relative Asymptotics for Orthogonal Matrix Polynomials with Convergent Recurrence Coefficients

The asymptotic behavior of #n (d;) #n (d:) and Pn (x, d;) P n (x, d:) is studied. Here (#n (.))n are the leading coefficients of the orthonormal matrix polynomials Pn (x, .) with respect to the matrix measures d; and d: which are related by d;(u)= d:(u)+ k=1 Mk$(u&ck), where Mk are positive definite matrices, $ is the Dirac measure and ck lies outside the support of d: for k=1, ..., N. Finally,...

On Sobolev type orthogonal polynomials with unbounded support: asymptotic properties

In this expository paper we present a survey about asymptotic properties of Sobolev type orthogonal polynomials with unbounded support.