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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
  • Barbara Martinucci

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 & Barbara Martinucci, 2022. "On Gaussian Hypergeometric Functions of Three Variables: Some New Integral Representations," Journal of Mathematics, Hindawi, vol. 2022, pages 1-16, August.
    • Handle: RePEc:hin:jjmath:1914498
    DOI: 10.1155/2022/1914498
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