IDEAS home Printed from https://ideas.repec.org/a/gam/jstats/v5y2022i4p72-1220d981467.html
   My bibliography  Save this article

On the Relation between Lambert W-Function and Generalized Hypergeometric Functions

Author

Listed:
  • Pushpa Narayan Rathie

    (Department of Statistics, University of Brasilia, Brasília 70910-900, Brazil
    These authors contributed equally to this work.)

  • Luan Carlos de Sena Monteiro Ozelim

    (Department of Civil and Environmental Engineering, University of Brasilia, Brasília 70910-900, Brazil
    These authors contributed equally to this work.)

Abstract

In the theory of special functions, finding correlations between different types of functions is of great interest as unifying results, especially when considering issues such as analytic continuation. In the present paper, the relation between Lambert W-function and generalized hypergeometric functions is discussed. It will be shown that it is possible to link these functions by following two different strategies, namely, by means of the direct and inverse Mellin transform of Lambert W-function and by solving the trinomial equation originally studied by Lambert and Euler. The new results can be used both to numerically evaluate Lambert W-function and to study its analytic structure.

Suggested Citation

  • Pushpa Narayan Rathie & Luan Carlos de Sena Monteiro Ozelim, 2022. "On the Relation between Lambert W-Function and Generalized Hypergeometric Functions," Stats, MDPI, vol. 5(4), pages 1-9, November.
    • Handle: RePEc:gam:jstats:v:5:y:2022:i:4:p:72-1220:d:981467
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2571-905X/5/4/72/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2571-905X/5/4/72/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Krishnaiah, P. R., 1976. "Some recent developments on complex multivariate distributions," Journal of Multivariate Analysis, Elsevier, vol. 6(1), pages 1-30, March.
    2. Dumitru Baleanu & Praveen Agarwal, 2014. "On Generalized Fractional Integral Operators and the Generalized Gauss Hypergeometric Functions," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-5, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bhandary, Madhusudan, 1996. "Test for generalized variance in signal processing," Statistics & Probability Letters, Elsevier, vol. 27(2), pages 155-162, April.
    2. Hélène Massam & Erhard Neher, 1997. "On Transformations and Determinants of Wishart Variables on Symmetric Cones," Journal of Theoretical Probability, Springer, vol. 10(4), pages 867-902, October.
    3. Daya K. Nagar & Alejandro Roldán-Correa & Saralees Nadarajah, 2023. "Expected Values of Scalar-Valued Functions of a Complex Wishart Matrix," Mathematics, MDPI, vol. 11(9), pages 1-14, May.
    4. Pushpa Narayan Rathie & Luan Carlos de Sena Monteiro Ozelim & Felipe Quintino & Tiago A. da Fonseca, 2023. "On the Extreme Value H -Function," Stats, MDPI, vol. 6(3), pages 1-10, August.
    5. Ahmed Bakhet & Abd-Allah Hyder & Areej A. Almoneef & Mohamed Niyaz & Ahmed H. Soliman, 2022. "On New Matrix Version Extension of the Incomplete Wright Hypergeometric Functions and Their Fractional Calculus," Mathematics, MDPI, vol. 10(22), pages 1-14, November.

    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:jstats:v:5:y:2022:i:4:p:72-1220:d:981467. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.