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Extended k-Gamma and k-Beta Functions of Matrix Arguments

Author

Listed:
  • Ghazi S. Khammash

    (Department of Mathematics, Al-Aqsa University, Gaza Strip 79779, Palestine)

  • Praveen Agarwal

    (Department of Mathematics, Anand International College of Engineering, Jaipur 303012, India
    Institute of Mathematics and Mathematical Modeling, Almaty 050010, Kazakhstan
    Harish-Chandra Research Institute Chhatnag Road, Jhunsi, Prayagraj (Allahabad) 211019, India)

  • Junesang Choi

    (Department of Mathematics, Dongguk University, Gyeongju 38066, Korea)

Abstract

Various k-special functions such as k-gamma function, k-beta function and k-hypergeometric functions have been introduced and investigated. Recently, the k-gamma function of a matrix argument and k-beta function of matrix arguments have been presented and studied. In this paper, we aim to introduce an extended k-gamma function of a matrix argument and an extended k-beta function of matrix arguments and investigate some of their properties such as functional relations, inequality, integral formula, and integral representations. Also an application of the extended k-beta function of matrix arguments to statistics is considered.

Suggested Citation

  • Ghazi S. Khammash & Praveen Agarwal & Junesang Choi, 2020. "Extended k-Gamma and k-Beta Functions of Matrix Arguments," Mathematics, MDPI, vol. 8(10), pages 1-13, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1715-:d:424137
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    References listed on IDEAS

    as
    1. Shahid Mubeen & Sana Iqbal & Gauhar Rahman, 2015. "Contiguous Function Relations and an Integral Representation for Appell k-Series F_(1,k)," International Journal of Mathematics Research, Conscientia Beam, vol. 4(2), pages 53-63.
    2. Constantine, A. G. & Muirhead, R. J., 1972. "Partial differential equations for hypergeometric functions of two argument matrices," Journal of Multivariate Analysis, Elsevier, vol. 2(3), pages 332-338, September.
    3. Shahid Mubeen & Sana Iqbal & Gauhar Rahman, 2015. "Contiguous Function Relations and an Integral Representation for Appell k-Series F_(1,k)," International Journal of Mathematical Research, Conscientia Beam, vol. 4(2), pages 53-63.
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    Cited by:

    1. Mohammed Z. Alqarni, 2024. "Exploring the Extended Beta-Logarithmic Function: Matrix Arguments and Properties," Mathematics, MDPI, vol. 12(11), pages 1-17, May.

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