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JOURNAL OF MATHEMATICAL CHEMISTRY, vol.37, no.4, pp.377-388, 2005 (SCI-Expanded)
This is the second in a series of papers dealing with the sets of orthogonal polynomials generated by a trigonometric Hamiltonian. In the first of this series, a subclass of the Jacobi polynomials denoted by T-n((u)) (x) and referred to as the T - polynomial of the first kind, which arises in the investigation of the symmetric state eigenfunctions of the Hamiltonian under consideration, was examined. Another subclass of the Jacobi polynomials denoted by U ((u))(n) (x) is introduced here representing the antisymmetric states, and is called in accordance the T - polynomial of the second kind. Moreover, by the derivation of the ultraspherical polynomial wavefunctions, interrelations between the T - polynomials of the first and second kinds as well as the other orthogonal polynomial systems are also emphasized.