Some multivariable orthogonal polynomials of the Askey tableau—Continuous families

A multivariable generalization is presented for all the continuous families of the Askey tableaux. This significantly extends some previously known multivariable Jacobi polynomials. The latter are recovered as a limit case from a family of multivariable continuous Hahn polynomials which in turn are obtained as a limit of some multivariable Wilson polynomials. A continuous analog of the single variable Charlier polynomials is also introduced.