1.Institut für Diskrete Mathematik und Geometrie,Technische Universit?t Wien,Wien,Austria;2.Institut für Mathematik A,Technische Universit?t Graz,Graz,Austria
Abstract:
It is well-known that Morgan-Voyce polynomials Bn(x) and bn(x) satisfy both a Sturm-Liouville equation of second order and a three-term recurrence equation ([SWAMY, M.: Further properties of Morgan-Voyce polynomials, Fibonacci Quart. 6 (1968), 167–175]). We study Diophantine equations involving these polynomials as well as other modified classical orthogonal polynomials with this property. Let A, B, C ∈ ? and {pk(x)} be a sequence of polynomials defined by