Biorthogonal polynomials suggested by the Jacobi polynomials

In this paper we introduce and study a pair of biorthogonal polynomials that are suggested by the classical Jacobi polynomials. Let a> -l,>-l and /""(, , k; x) and K n {a, , k; x), n=0,1, 2, be respectively the polynomials of degree n in x k and x, where x is real, k is a positive integer such that these two polynomial sets satisfy biorthogonality conditions with respect to the weight function (1-x) a (l+x) , namely