Evaluation of certain class of Eulerian integrals of multivariable Sister Celine' s polynomials

Abstract

In this paper, we evaluate a key Eulerian integral involving Sister Celine's polynomials of several complex variables defined by the author. Our general Eulerian integral formula are shown to provide the key formula from which numerous other potentially useful results involving polynomials such as Jacobi, Laguerre, Hermite, Bessel, Bateman, Rice etc and also discrete polynomials like Hahn, Krawtchouk, Pasternak, Meixner, Poisson-Charlier are derived.