A class of generating functions for Chebshev polynomials by Weisner method

Abstract

In this paper, an attempt has been made to obtain generating functions for the Chebyshev polynomials Tn (x) (Special ultra spherical polynomials of first kind) using Weisner’s group-theoretic method by interpreting ‘n’ suitably. It is possible to derive at least three generating relations for various special functions of mathematical physics using this method introduced by Louis Weisner. In approximation theory, the roots (nodes) of Tn(x) are used as matching-points for optimizing polynomial interpolation. Chebyshev polynomials are also used in many models to study them elegantly.