IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i19p3547-d928504.html
   My bibliography  Save this article

General Master Theorems of Integrals with Applications

Author

Listed:
  • Mohammad Abu-Ghuwaleh

    (Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan)

  • Rania Saadeh

    (Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan)

  • Ahmad Qazza

    (Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan)

Abstract

Many formulas of improper integrals are shown every day and need to be solved in different areas of science and engineering. Some of them can be solved, and others require approximate solutions or computer software. The main purpose of this research is to present new fundamental theorems of improper integrals that generate new formulas and tables of integrals. We present six main theorems with associated remarks that can be viewed as generalizations of Cauchy’s results and I.S. Gradshteyn integral tables. Applications to difficult problems are presented that cannot be solved with the usual techniques of residue or contour theorems. The solutions of these applications can be obtained directly, depending on the proposed theorems with an appropriate choice of functions and parameters.

Suggested Citation

  • Mohammad Abu-Ghuwaleh & Rania Saadeh & Ahmad Qazza, 2022. "General Master Theorems of Integrals with Applications," Mathematics, MDPI, vol. 10(19), pages 1-19, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3547-:d:928504
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/19/3547/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/19/3547/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Chunli Li & Wenchang Chu, 2022. "Evaluation of Infinite Series by Integrals," Mathematics, MDPI, vol. 10(14), pages 1-14, July.
    2. 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.
    3. Ahmad Qazza & Aliaa Burqan & Rania Saadeh, 2021. "A New Attractive Method in Solving Families of Fractional Differential Equations by a New Transform," Mathematics, MDPI, vol. 9(23), pages 1-14, November.
    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. Abu-Ghuwaleh, Mohammad & Saadeh, Rania & Saffaf, Rasheed, 2024. "Master generators: A novel approach to construct and solve ordinary differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 600-623.

    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. Rania Saadeh & Ahmad Qazza & Aliaa Burqan, 2022. "On the Double ARA-Sumudu Transform and Its Applications," Mathematics, MDPI, vol. 10(15), pages 1-19, July.
    2. Chunli Li & Wenchang Chu, 2022. "Evaluation of Infinite Series by Integrals," Mathematics, MDPI, vol. 10(14), pages 1-14, July.

    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:19:p:3547-:d:928504. 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.