Application of a finite class of orthogonal polynomials related to T-student distribution in spectral methods

Classical orthogonal polynomials play an important role in science and engineering. These polynomials are divided into two parts; the infinite and finite sequences of orthogonal polynomials. In this paper, we present a sequence of orthogonal polynomials (I(p) n (x)) which is finitely orthogonal with respect to T-student distribution on infinite interval (−∞,+∞). In doing so, in the first part of the paper, general properties of this sequence such as orthogonality relation, Rodrigues type formula, recurrence relations and also some of its applications such as Gauss quadrature formulas and so on are indicated. In addition, in the second part, we show how one can apply I(p) n (x) in approximations and particularly in spectral methods. Error analysis and convergence of the method are thoroughly investigated. At the end, two numerical examples are given for the efficiency and accuracy of the proposed method. In conclusion, the finite class of orthogonal polynomials related to T-student distribution provides an efficient spectral method on unbounded domain.