Continued-fraction expansions for ratios of generalized polynomials

摘要

Continued-fraction expansions of Stieltjes and second Cauer from are considered for a ratio of polynomials expressed relative to an arbitrary real orthogonal polynomials basis. Simple tabular arrays are developed for obtaining the coefficients in the expansions. Inverse procedures are also obtained. An application to a diophantine equation, and corresponding results for matrix continued fractions, are also given.