Title | Analytic properties of some basic hypergeometric-Sobolev-type orthogonal polynomials |
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Authors | COSTAS SANTOS, ROBERTO SANTIAGO, Soria-Lorente, Anier |

External publication | Si |

Means | JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS |

Scope | Article |

Nature | Científica |

JCR Quartile | 3 |

SJR Quartile | 2 |

JCR Impact | 0.974 |

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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