Generating Function of some Biorthogonal Polynomials Involving Stirling Numbers of Second Kind

In 1982 Madhekar and Thakare defined and studied a pair of biorthogonal polynomials {Jn(α, β, k; x)} and {Kn(α, β, k; x)} with respect to Jacobi weight function (1-x)α (1+x)β over the interval (-1, 1) where α > -1; β > -1 and k is positive integer. In the present paper some generating functions of biorthogonal polynomials of second set {Kn(α, β, k; x)} involving Stirling numbers of second kind are obtained by using Srivastava's method and some particular cases are also noted.