Recurrence techniques for the calculation of bessel functions

Abstract

where Fv(x) may be either J,(x) or Y,(x). If one is given Y,(x) and Yv+?(x) then Eq. (1) may be used to generate the functions Yv+,(x). For ? >> (x/2) the function Y,(x) increases extremely rapidly with increasing order, i.e., Y,(x) -(2,u/x) and the functions Y,+n(x) calculated from Eq. (1) yield good accuracy for large n. However, if one is given JA(x) and J,+? (x), Eq. (1) gives poor accuracy for Jv+n(x), since for ? >> (x/2), J,(x) -(2l/x)->. On the other hand, if one is given Jv+n(x) and Jv+n+l(x), where n >> (x/2), then one may again recur without loss of accuracy but this time in the direction of decreasing order. We shall first treat the problem of using the recurrence technique in the calculation of the regular Bessel function Jv+n(x). Thus, let us find Jv+n(x), for 0 < v < 1 and n < N.