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On Gaussian Hypergeometric Functions of Three Variables: Some New Integral Representations

Author

Listed:
  • Maged G. Bin-Saad
  • Mohannad J. S. Shahwan
  • Jihad A. Younis
  • Hassen Aydi
  • Mohamed A. Abd El Salam

Abstract

The present paper establishes several new integral representations of the Euler type and Laplace type for some Gauss hypergeometric functions of three variables. The main results are obtained by using the properties of Gamma and beta functions. The novel integral representations are carried out through ten hypergeometric functions of three variables. Therefore, all derived integrals are generalization representation of the Euler type for the classical Gauss hypergeometric function of one and two variables. In addition, several numerical examples were given to describe some of the obtained results.

Suggested Citation

  • Maged G. Bin-Saad & Mohannad J. S. Shahwan & Jihad A. Younis & Hassen Aydi & Mohamed A. Abd El Salam, 2022. "On Gaussian Hypergeometric Functions of Three Variables: Some New Integral Representations," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:1914498
    DOI: 10.1155/2022/1914498
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    References listed on IDEAS

    as
    1. Hari Mohan Srivastava & Asifa Tassaddiq & Gauhar Rahman & Kottakkaran Sooppy Nisar & Ilyas Khan, 2019. "A New Extension of the τ -Gauss Hypergeometric Function and Its Associated Properties," Mathematics, MDPI, vol. 7(10), pages 1-9, October.
    2. Jihad A. Younis & Hassen Aydi & Ashish Verma & Ahmet Ocak Akdemir, 2021. "Some Formulas for New Quadruple Hypergeometric Functions," Journal of Mathematics, Hindawi, vol. 2021, pages 1-10, April.
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