Use of Convergent and Asymptotic Series for Computation of the Modified Bessel Function of the First Kind. (open access)

Use of Convergent and Asymptotic Series for Computation of the Modified Bessel Function of the First Kind.

In the Communications of the ACM of April, 1960, p. 240, there appeared two Algol algorithms for the computation of In, the modified Bessel function of the first kind. One of these algorithms uses a convergent series and the other an asymptotic series. Their author, Dorothea S. Clarke, did not give any information with regard to which algorithm is more appropriate in a given situation (a given situation meaning the computation of In (x) for a definite pair of numbers n and x). Such information is necessary, however, if the algorithms are to be useful, particularly since the asymptotic series is in many cases not valid.
Date: December 12, 1960
Creator: Bumgarner, L. L.
System: The UNT Digital Library