On Generating Bessel Functions by Use of the Backward Recurrence Formula
Abstract
In the author's work, The Special Functions and Their Approximations, a class of rational approximations for the generalized hypergeometric functions was developed. Now I(sub nu)(Z) can be expressed in terms of a sub 0(F)sub 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 I(sub nu)(Z). J. C. P. Miller has shown that I sub(m+nu)(Z), m a positive integer or zero, can be approximated by use of the recursion formula for I sub(m+nu)(Z) applied in the backward direction. If this scheme is used together with each of two certain normalization relations, then rational approximations for I(sub nu)(Z) 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 sub(m+nu)(Z), m a positive integer, by the backward recursion process which presumes that I(sub nu)(Z) is know.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 15, 1971
- Accession Number
- AD0734797
Entities
People
- Yudell L. Luke