A (p, ν)-extension of the Appell function F1(·) and its properties

S. A. Dar*, R. B. Paris

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    5 Citations (Scopus)
    100 Downloads (Pure)


    In this paper, we obtain a (p, v)-extension of the Appell hypergeometric function
    F1(·), together with its integral representation, by using the extended Beta function
    Bp,v(x, y) introduced in [9]. Also, we give some of its main properties, namely the
    Mellin transform, a differential formula, recursion formulas and a bounded inequality. In addition, some new integral representations of the extended Appell functionF1,p,v(·) involving Meijer’s G-function are obtained.
    Original languageEnglish
    Pages (from-to)12-19
    Number of pages8
    JournalJournal of Computational and Applied Mathematics
    Early online date12 Mar 2019
    Publication statusPublished - 1 Oct 2019


    • Appell’s hypergeometric functions
    • Beta and gamma functions
    • Eulerian integrals
    • Bessel function
    • Meijer’s G-function


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