Bulletin of the Korean Mathematical Society (대한수학회보)

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EXTENSIONS OF MULTIPLE LAURICELLA AND HUMBERT'S CONFLUENT HYPERGEOMETRIC FUNCTIONS THROUGH A HIGHLY GENERALIZED POCHHAMMER SYMBOL AND THEIR RELATED PROPERTIES

  • Ritu Agarwal (Department of Mathematics Malaviya National Institute of Technology) ;
  • Junesang Choi (Department of Mathematics Dongguk University) ;
  • Naveen Kumar (Department of Mathematics Malaviya National Institute of Technology) ;
  • Rakesh K. Parmar (Department of HEAS (Mathematics) University College of Engineering and Technology and Department of Mathematics Ramanujan School of Mathematical Sciences Pondicherry University-A Central University)
  • Received : 2021.09.01
  • Accepted : 2023.03.10
  • Published : 2023.05.31
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Abstract

Motivated by several generalizations of the Pochhammer symbol and their associated families of hypergeometric functions and hypergeometric polynomials, by choosing to use a very generalized Pochhammer symbol, we aim to introduce certain extensions of the generalized Lauricella function F(n)A and the Humbert's confluent hypergeometric function Ψ(n) of n variables with, as their respective particular cases, the second Appell hypergeometric function F2 and the generalized Humbert's confluent hypergeometric functions Ψ2 and investigate their several properties including, for example, various integral representations, finite summation formulas with an s-fold sum and integral representations involving the Laguerre polynomials, the incomplete gamma functions, and the Bessel and modified Bessel functions. Also, pertinent links between the major identities discussed in this article and different (existing or novel) findings are revealed.

Keywords

Acknowledgement

The fourth-named author has carried out this research under the project MATRICS, SERB, Department of Science & Technology (DST), India (File No. MTR/2019/001328).

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