Computation of Scattering Coefficients and Cross Sections

Aden (1951) was apparently the first to introduce the logarithmic derivative 

There are two possible schemes for calculating Dn mx) in (4.88) upward recurrence (higher orders are generated from lower orders) and downward 

In the light of the preceding paragraph it appears that the most conservative method for computing scattering coefficients is to compute Dn and jn by downward recurrence and yn by upward recurrence (recall that 4 n = pj and 

Wiscombe (1979, 1980) has recently discussed very thoroughly many of the problems encountered in computing scattering coefficients and has suggested techniques for greatly increasing the speed of such computations. 

Caution Even if Dn and jn are calculated by downward recurrence and y by upward recurrence with as much precision as can be squeezed out of the largest 

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