A class of orthogonal polynomials suggested by a trigonometric Hamiltonian : Symmetric states

Taseli H.

JOURNAL OF MATHEMATICAL CHEMISTRY, vol.36, no.1, pp.1-12, 2004 (SCI-Expanded) identifier identifier


A new subclass of the Jacobi polynomials arising in the exact analytical solution of the one-dimensional Schrodinger equation with a trigonometric potential has been introduced. The polynomials which consist of a free parameter are not ultraspherical polynomials and have been simply named the T - polynomials since they are generated by a trigonometric Hamiltonian. In certain sense, it is shown that the T - polynomials can be regarded as a generalisation of the airfoil polynomials or the Chebyshev polynomials of the third kind. This paper is intended to discuss the basic properties of the polynomials so defined.