• 대한수학회보
• /
• 제60권3호
• /
• pp.575-591
• /
• 2023

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.

• Kyungpook Mathematical Journal
• /
• 제47권4호
• /
• pp.495-500
• /
• 2007

The aim of this paper is to derive a fractional derivative of the multivariable H-function of Srivastava and Panda [7], associated with a general class of multivariable polynomials of Srivastava [4] and the generalized Lauricella functions of Srivastava and Daoust [9]. Certain special cases have also been discussed. The results derived here are of a very general nature and hence encompass several cases of interest hitherto scattered in the literature.

• 대한수학회논문집
• /
• 제28권4호
• /
• pp.783-797
• /
• 2013

Recently, Liu et al. [Bilateral generating functions for the Chan-Chyan-Srivastava polynomials and the generalized Lauricella function, Integral Transform Spec. Funct. 23 (2012), no. 7, 539-549] investigated, in several interesting papers, some various families of bilateral generating functions involving the Chan-Chyan-Srivastava polynomials. The aim of this present paper is to obtain some bilateral generating functions involving the Chan-Chyan-Sriavastava polynomials and three general classes of multivariable polynomials introduced earlier by Srivastava in [A contour integral involving Fox's H-function, Indian J. Math. 14 (1972), 1-6], [A multilinear generating function for the Konhauser sets of biorthogonal polynomials suggested by the Laguerre polynomials, Pacific J. Math. 117 (1985), 183-191] and by Kaano$\breve{g}$lu and $\ddot{O}$zarslan in [Two-sided generating functions for certain class of r-variable polynomials, Mathematical and Computer Modelling 54 (2011), 625-631]. Special cases involving the (Srivastava-Daoust) generalized Lauricella functions are also given.

• Kyungpook Mathematical Journal
• /
• 제45권4호
• /
• pp.471-480
• /
• 2005

This paper deals with some useful methods of solving the one-dimensional integral equation of Fredholm type. Application of the reduction techniques with a view to inverting a class of integral equation with Lauricella function in the kernel, Riemann-Liouville fractional integral operators as well as Weyl operators have been made to reduce to this class to generalized Stieltjes transform and inversion of which yields solution of the integral equation. Use of Mellin transform technique has also been made to solve the Fredholm integral equation pertaining to certain polynomials and H-functions.