Also note that cos m<j> = cos((m — 1 )<f> + <j>)

= cos((m— 1 )<f>)cos <f> — sin<£sin((m— 1)<£)

A similar recursion relation can be derived for sinm<i>. The computational advantage of Eq. (H-ll) is that it greatly reduces the number of times that sine and cosine functions must be calculated.

Given the coefficients gnm and hnm and recursion relations in Eqs. (H-7) through (H-l 1). the field B is calculated from Eqs. (H-l) and (H-2). Specifically,

2 (-)" (n+l) 2 (g"'mcosm<l>+ hn,msmm$)Pn-m(0)

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