Group theoretic study of certain generalised functions of Jacobi polynomial

Abstract

Making suitable interpretations to both the index  (n)  and the parameter (Beta) of Jacobi polynomials  Pn (alpha, beta)  in order to derive the elements of Lie-algebra, we have constructed a four parameter Lie-group  for this polynomials which does not seem to appear before. By means of group-theoretic method  a new generating function for Jacobi polynomials is obtained, from which several special generating  functions can easily be derived