On the first set J_n (α,β,K;x) of Bi-orthogonal Polynomials suggested by the Jacobi Polynomials

Abstract

Madhekar and Thakare succeeded in constructing a pair of bi-orthogonal polynomials  and  that are suggested by Jacobi polynomials. In the sense that for  both these polynomials reduces to Jacobi polynomials. Madhekar and Thakare obtained recurrence relations, operational formulae, generating functions, bi-orthogonality, multilinear and multilateral generating function involving bi-orthogonal polynomials suggested by Jacobi polynomials. Dhanorkar and Kavthekar [3] worked on biorthogonal polynomials for the weight function . In the present paper we obtained some interesting results with some particular cases for the first set . In which generating function is obtained from hypergeometric function and Manocha [8]. Also find recurrence relation from Rainville [10].