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A Continued Fraction Algorithm for the Computation of Higher Transcendental Functions in the Complex Plane

I. Gargantini and P. Henrici
Mathematics of Computation
Vol. 21, No. 97 (Jan., 1967), pp. 18-29
DOI: 10.2307/2003467
Stable URL: http://www.jstor.org/stable/2003467
Page Count: 12
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A Continued Fraction Algorithm for the Computation of Higher Transcendental Functions in the Complex Plane
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Abstract

This report deals with the numerical evaluation of a class of functions of a complex variable that can be represented as Stieltjes transforms of non-negative real functions. The considered class of functions contains, among others, the confluent hypergeometric functions of Whittaker and the Bessel functions. The method makes it possible, in principle, to compute the values of the function with an arbitrarily small error, using one and the same algorithm in whole complex plane cut along the negative real axis. Detailed numerical data are given for the application of the algorithm to the modified Bessel function K0(z).

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