IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i16p1952-d615013.html
   My bibliography  Save this article

Infinite Sum of the Incomplete Gamma Function Expressed in Terms of the Hurwitz Zeta Function

Author

Listed:
  • Robert Reynolds

    (Department of Mathematics and Statistics, York University, Toronto, ON M3J1P3, Canada)

  • Allan Stauffer

    (Department of Mathematics and Statistics, York University, Toronto, ON M3J1P3, Canada)

Abstract

We apply our simultaneous contour integral method to an infinite sum in Prudnikov et al. and use it to derive the infinite sum of the Incomplete gamma function in terms of the Hurwitz zeta function. We then evaluate this formula to derive new series in terms of special functions and fundamental constants. All the results in this work are new.

Suggested Citation

  • Robert Reynolds & Allan Stauffer, 2021. "Infinite Sum of the Incomplete Gamma Function Expressed in Terms of the Hurwitz Zeta Function," Mathematics, MDPI, vol. 9(16), pages 1-7, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1952-:d:615013
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/16/1952/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/16/1952/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Bailey, D.H. & Borwein, J.M., 2015. "Crandall’s computation of the incomplete Gamma function and the Hurwitz zeta function, with applications to Dirichlet L-series," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 462-477.
    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.

      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:16:p:1952-:d:615013. 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.