IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i14p2444-d861931.html
   My bibliography  Save this article

Evaluation of Infinite Series by Integrals

Author

Listed:
  • Chunli Li

    (School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China)

  • Wenchang Chu

    (Department of Mathematics and Physics, University of Salento, 73100 Lecce, Italy)

Abstract

We examine a large class of infinite triple series and establish a general summation formula. This is done by expressing the triple series in terms of definite integrals involving arctangent function that are evaluated in turn in closed forms. Numerous explicit formulae are tabulated for the triple series whose values result in elegant expressions as π , ln 2 and the Catalan constant G .

Suggested Citation

  • Chunli Li & Wenchang Chu, 2022. "Evaluation of Infinite Series by Integrals," Mathematics, MDPI, vol. 10(14), pages 1-14, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:14:p:2444-:d:861931
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/14/2444/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/14/2444/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jocemar Q. Chagas & José A. Tenreiro Machado & António M. Lopes, 2022. "Revisiting the Formula for the Ramanujan Constant of a Series," Mathematics, MDPI, vol. 10(9), pages 1-15, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Mohammad Abu-Ghuwaleh & Rania Saadeh & Ahmad Qazza, 2022. "General Master Theorems of Integrals with Applications," Mathematics, MDPI, vol. 10(19), pages 1-19, September.

    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. Mohammad Abu-Ghuwaleh & Rania Saadeh & Ahmad Qazza, 2022. "General Master Theorems of Integrals with Applications," Mathematics, MDPI, vol. 10(19), pages 1-19, September.

    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:10:y:2022:i:14:p:2444-:d:861931. 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.