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Two-Variable q -General-Appell Polynomials Within the Context of the Monomiality Principle

Author

Listed:
  • Noor Alam

    (Department of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi Arabia)

  • Waseem Ahmad Khan

    (Department Electrical Engineering, Prince Mohammad Bin Fahd University, P.O. Box 1664, Al Khobar 31952, Saudi Arabia)

  • Can Kızılateş

    (Department of Mathematics, Faculty of Science, Zonguldak Bülent Ecevit University, Zonguldak 67100, Turkey)

  • Cheon Seoung Ryoo

    (Department of Mathematics, Hannam University, Daejeon 34430, Republic of Korea)

Abstract

In this study, we consider the two-variable q -general polynomials and derive some properties. By using these polynomials, we introduce and study the theory of two-variable q -general Appell polynomials (2V q gAP) using q -operators. The effective use of the q -multiplicative operator of the base polynomial produces the generating equation for 2V q gAP involving the q -exponential function. Furthermore, we establish the q -multiplicative and q -derivative operators and the corresponding differential equations. Then, we obtain the operational, explicit and determinant representations for these polynomials. Some examples are constructed in terms of the two-variable q -general Appell polynomials to illustrate the main results. Finally, graphical representations are provided to illustrate the behavior of some special cases of the two-variable q -general Appell polynomials and their potential applications.

Suggested Citation

  • Noor Alam & Waseem Ahmad Khan & Can Kızılateş & Cheon Seoung Ryoo, 2025. "Two-Variable q -General-Appell Polynomials Within the Context of the Monomiality Principle," Mathematics, MDPI, vol. 13(5), pages 1-21, February.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:5:p:765-:d:1600152
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    References listed on IDEAS

    as
    1. Subuhi Khan & Nusrat Raza, 2013. "General-Appell Polynomials within the Context of Monomiality Principle," International Journal of Analysis, Hindawi, vol. 2013, pages 1-11, February.
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