On a singular integral equation including a set of multivariate polynomials suggested by Laguerre polynomials

In this paper, we introduce the class of polynomials Zn1,…,nj(α)(x1,…,xj;ρ1,…,ρj) suggested by the multivariate Laguerre polynomials. We give Schläfli's contour integral representation and calculate the fractional order integral of these polynomials. Furthermore, we obtain linear, multilinear and mixed multilateral generating functions for them. Finally, we construct a singular integral equation with Zn1,…,nj(α)(x1,…,xj;ρ1,…,ρj) in the kernel and obtain the solution in terms of multivariate analogue of the Mittag-Leffler functions.