COSTAS SANTOS, ROBERTO SANTIAGO, Soria-Lorente, Anier
Si
J. Differ. Equ. Appl.
Article
Científica
0.974
02/11/2018
000452176500001
2-s2.0-85053299501
In this contribution, we consider sequences of monic polynomials orthogonal with respect to a Sobolev-type inner product < f,g > s := < u,fg > + N(D(q)f)(alpha)(D(q)g)(alpha), alpha is an element of R, N >= 0, where u is a q-classical linear functional and D-q is the q-derivative operator. We obtain some algebraic properties of these polynomials such as an explicit representation, a five-term recurrence relation as well as a second order linear q-difference holonomic equation fulfilled by such polynomials. We present an analysis of the behaviour of its zeros as a function of the mass N. In particular, we obtain the exact values of N such that the smallest (respectively, the greatest) zero of the studied polynomials is located outside of the support of the measure. We conclude this work by considering two examples.
Classical orthogonal polynomials; Sobolev-type orthogonal polynomials; basic Hypergeometric series; zeros