Edmundo Huertas Cejudo

27/10/2020
Speaker: Edmundo Huertas Cejudo
Title: A generalization of Jacobi continued fractions for non-standard Sobolev-type orthogonal polynomials.
Abstract: In the celebrated Chihara’s book on orthogonal polynomials, one can finds (Chapter III) a beautiful relation between standard orthogonal polynomials and continued fractions. This relation flows through the coefficients of the 3TRR satisfied by (all) the standard orthogonal polynomials sequences. Using certain three term recurrence formula with rational coefficients, satisfied by a good number of non-standard Sobolev-type orthogonal sequences, we find a simple extension of the aforesaid relation between orthogonal polynomials and continued fractions. We present a particular example using Al-Salam–Carlitz I-Sobolev-type orthogonal polynomials of higher order. This is a joint work with Anier Soria-Lorente, Alberto Lastra and Carlos Hermoso.