OICC Press Journal of Theoretical and Applied Physics 2251-7235 19 2 2025 04 10 Application of a finite class of orthogonal polynomials related to T-student distribution in spectral methods 1 15 10.57647/j.jtap.2025.1902.22 EN Amir Hossein Salehi Shayegan Mathematics Department, Faculty of Basic Science, Khatam-ol-Anbia (PBU) University, Tehran, Iran. https://orcid.org/0000-0002-6077-5321 Journal Article 2025 04 10 Classical orthogonal polynomials play an important role in science and engineering. These polynomialsare divided into two parts; the infinite and finite sequences of orthogonal polynomials. In this paper, wepresent a sequence of orthogonal polynomials (I(p)n (x)) which is finitely orthogonal with respect to T-studentdistribution on infinite interval (−∞,+∞). In doing so, in the first part of the paper, general properties of thissequence such as orthogonality relation, Rodrigues type formula, recurrence relations and also some of itsapplications such as Gauss quadrature formulas and so on are indicated. In addition, in the second part, weshow how one can apply I(p)n (x) in approximations and particularly in spectral methods. Error analysis andconvergence of the method are thoroughly investigated. At the end, two numerical examples are given for theefficiency and accuracy of the proposed method. In conclusion, the finite class of orthogonal polynomialsrelated to T-student distribution provides an efficient spectral method on unbounded domain.