IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-030-40120-7_7.html
   My bibliography  Save this book chapter

Formulas and Inequalities for Some Special Functions of a Complex Variable

In: Advancements in Complex Analysis

Author

Listed:
  • Arcadii Z. Grinshpan

    (University of South Florida, Department of Mathematics and Statistics)

Abstract

The presented formulas and inequalities are based on interconnection of convolution and hypergeometric properties. Some known transformations and a direct coefficient technique are combined to analyze and structure a parameterized product identity involving three Gauss hypergeometric functions. A convolution presentation of this identity is a generalization of the Bateman and Kapteyn integrals for Bessel functions as well as of the addition theorem for the confluent hypergeometric functions. These results and integral properties of weighted convolutions lead to multiparameter weighted norm inequalities for generalized hypergeometric functions and special functions of hypergeometric type, in particular, for Bessel and Whittaker functions, and Laguerre and Hermite polynomials.

Suggested Citation

  • Arcadii Z. Grinshpan, 2020. "Formulas and Inequalities for Some Special Functions of a Complex Variable," Springer Books, in: Daniel Breaz & Michael Th. Rassias (ed.), Advancements in Complex Analysis, pages 299-318, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-40120-7_7
    DOI: 10.1007/978-3-030-40120-7_7
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:spr:sprchp:978-3-030-40120-7_7. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.