In this paper we study a set of orthogonal Polynomials with respect a certain given measure related to the Taylor series expansion of the Xi-function , this paper is based on a previous conjecture by Carlon and Gaston related to the fact that Riemann Hypothesis (with simple zeros) is equivalent to the limit for a certain set of orthogonal Polynomials, we study the 'Hamburger moment problem' for even 'n' and 0 for n odd here the moments are related to the power series expansion of Xi-function , we also give the integral representation for the generating function , in terms of the Laplace transform of , and in the end of the paper we study the connection of our orthogonal polynomial set with the Kernel , through all the paper we will use the simplified notation (see paper for abstract with equations)