SOME APPLICATIONS OF THE LAGRANGE EXPANSION THEOREM ASSOCIATED WITH GENERAL POLYNOMIAL SYSTEMS

In this article, the author investigates several applications of the Lagrange expansion theorem involving such classical orthogonal polynomials as those that are popularly known as the Jacobi polynomials, the Laguerre polynomials, the Hermite polynomials and the Bessel polynomials. It is shown how some of these applications of the Lagrange expansion theorem would lead to many presumably new results associated with various general systems of polynomials. The results as well as the methods and techniques used for their derivations, which are presented here, are potentially useful in providing incentive and motivation for further researches on the subject investigated in this article.