Title Analytic properties of some basic hypergeometric-Sobolev-type orthogonal polynomials
Authors COSTAS SANTOS, ROBERTO SANTIAGO, Soria-Lorente, Anier
External publication Si
Means J. Differ. Equ. Appl.
Scope Article
Nature Científica
JCR Quartile 3
SJR Quartile 2
JCR Impact 0.97400
Web https://www.scopus.com/inward/record.uri?eid=2-s2.0-85053299501&doi=10.1080%2f10236198.2018.1517760&partnerID=40&md5=9c6ef3bd60216de25886dc9103655d11
Publication date 02/11/2018
ISI 000452176500001
Scopus Id 2-s2.0-85053299501
DOI 10.1080/10236198.2018.1517760
Abstract In this contribution, we consider sequences of monic polynomials orthogonal with respect to a Sobolev-type inner product\n < f,g > s := < u,fg > + N(D(q)f)(alpha)(D(q)g)(alpha), alpha is an element of R, N >= 0,\n 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.
Keywords Classical orthogonal polynomials; Sobolev-type orthogonal polynomials; basic Hypergeometric series; zeros
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