On Generating Bessel Functions by Use of the Backward Recurrence Formula
MISSOURI UNIV-KANSAS CITY DEPT OF MATHEMATICS
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In the authors work, The Special Functions and Their Approximations, a class of rational approximations for the generalized hypergeometric functions was developed. Now Isub nuZ can be expressed in terms of a sub 0Fsub 1 or a sub 1 F sub 1. Thus, corresponding to each form and a choice of certain free parameters there is a rational approximation for Isub nuZ. J. C. P. Miller has shown that I submnuZ, m a positive integer or zero, can be approximated by use of the recursion formula for I submnuZ applied in the backward direction. If this scheme is used together with each of two certain normalization relations, then rational approximations for Isub nuZ emerge and these rational approximations are identical with those noted above. The analysis leads to a new interpretation of the backward recursion scheme. The author also studies a third case for the evaluation of I submnuZ, m a positive integer, by the backward recursion process which presumes that Isub nuZ is know.
- Numerical Mathematics