33 



Substituting these results in Equation [81], we have 



.P-.n.(^.__)| 



[84a] 



[84b] 



+ P^+isin 



The associated Legendre function P^ is of the form 



c s\n^Qf{cos&) 

 in which /(cos 0) has the property that 



/(cos 0)^0 



Hence, we can divide Equation [84] through by sin*0 and set Q equal to zero to find <z* . 

 We make use of the recurrence relation 



2s cos 6 Pl = sin d P^+^ + (n + s) (n - s + 1) sin d P^~^ [85] 



Then 



\sin^ 0/ 2s \sin^+i 61/ 2 s Vsin^-^^' 



from which 



Pi \ {n+ s)(n- s+D / Pi~^ \ {n+s)\ 



I PI \ _{n+ s)(n- s + I) / PI ' \ 



[86] 



6=0 2 s ^sin ^'^=0 ^^'-(n-sy. 



