IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i9p955-d542879.html
   My bibliography  Save this article

On Certain Properties and Applications of the Perturbed Meixner–Pollaczek Weight

Author

Listed:
  • Abey S. Kelil

    (Department of Mathematics and Applied Mathematics, Nelson Mandela University, Port Elizabeth 6019, South Africa)

  • Alta S. Jooste

    (Department of Mathematics and Applied Mathematics, University of Pretoria, Hatfield 0028, South Africa)

  • Appanah R. Appadu

    (Department of Mathematics and Applied Mathematics, Nelson Mandela University, Port Elizabeth 6019, South Africa)

Abstract

This paper deals with monic orthogonal polynomials orthogonal with a perturbation of classical Meixner–Pollaczek measure. These polynomials, called Perturbed Meixner–Pollaczek polynomials, are described by their weight function emanating from an exponential deformation of the classical Meixner–Pollaczek measure. In this contribution, we investigate certain properties such as moments of finite order, some new recursive relations, concise formulations, differential-recurrence relations, integral representation and some properties of the zeros (quasi-orthogonality, monotonicity and convexity of the extreme zeros) of the corresponding perturbed polynomials. Some auxiliary results for Meixner–Pollaczek polynomials are revisited. Some applications such as Fisher’s information, Toda-type relations associated with these polynomials, Gauss–Meixner–Pollaczek quadrature as well as their role in quantum oscillators are also reproduced.

Suggested Citation

  • Abey S. Kelil & Alta S. Jooste & Appanah R. Appadu, 2021. "On Certain Properties and Applications of the Perturbed Meixner–Pollaczek Weight," Mathematics, MDPI, vol. 9(9), pages 1-28, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:9:p:955-:d:542879
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/9/955/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/9/955/
    Download Restriction: no
    ---><---

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:9:p:955-:d:542879. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.