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An Application of Separate Convergence for Continued Fractions to Orthogonal Polynomials

Abstract It is known that the n-th denominators Qn (α, β, z) of a real J-fraction where form an orthogonal polynomial sequence (OPS) with respect to a distribution function ψ(t) on ℝ. We use separate convergence results for continued fractions to prove the asymptotic formula the convergence being uniform on compact subsets of