Computation of special functions by Padé approximants with orthogonal polynomial denominators

This paper deals with the computation of special functions of mathematics and physics in the complex domain using continued fraction (one-point or two-point Padé) approximants. We consider three families of continued fractions (Stieltjes fractions, real J-fractions and non-negative T-fractions) whose denominators are orthogonal polynomials or Laurent polynomials. Orthogonality of these denominators plays an important role in the analysis of errors due to numerical roundoff and truncation of infinite sequences of approximants. From the rigorous error bounds described one can determine the exact number of significant decimal digits contained in the approximation of a given function value. Results from computational experiments are given to illustrate the methods.

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