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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

A continued fraction algorithm for the computation of higher transcendental functions in the complex plane
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by I. Gargantini and P. Henrici PDF
Math. Comp. 21 (1967), 18-29 Request permission

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 nonnegative 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 ${K_0}(z)$.
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Additional Information
  • © Copyright 1967 American Mathematical Society
  • Journal: Math. Comp. 21 (1967), 18-29
  • MSC: Primary 65.25; Secondary 41.00
  • DOI: https://doi.org/10.1090/S0025-5718-1967-0240950-1
  • MathSciNet review: 0240950