Summation formulas using a new class of special polynomials

In this paper we used a new class of special polynomials which satisfy a Sturm Liouville differential equation of second order. These polynomials form a basis of a polynomial space. Using coefficients of these polynomials we formed a lower triangular matrix which represents a transition matrix from standard polynomial basis to this new basis. Using Matlab for given natural number we obtained a corresponding matrix, found an inverse of this matrix, their eigenvalues and some interesting properties. Using a new class of special polynomials we obtained some interesting and useful summation formulas.