Thus we can express P*(X,Y,f) as complex infinite series with unknown 

 coefficients ag, a,, a™,... and b^^, b2, ... and constants defined 

 by the integrals (let 2 = ZttKD; n = 0, 1, 2, ...) of the form 



jcosr}eco5(iiCos(e--^))£i( 



... '® (7.19) 



(7.20) 



\&iM>ts Cfls(jLCos(e-"4f))Ae 

 Jcos>iesiN(3LCos(e-7|rMe 



(7.21) 



ay»cl 



fir 



(7.22) 





Consider Equation (7.19) where ^ = (O-ij)) and d(}) = dO, i|) being a constant. 

 We then have on changing variables 



= COS >j\|fJcos>icpctf5(ico5(f)dL(p 



(7.23) 





{■I * V 

 smr)(}cos(iC^S(p)d(f 



Since the integrands in Equation (7.23) are both of period 2tt and the 

 interval [-Tr-ip, ir-<J;] is of length 2tt we can write the equivalent of 

 Equation (7.23) as 



cosyt4>(cos»ipcos(iLCos<P)A(p 

 — Sin r\ H) (sin y\^ cos (z cos 4>) i(J 



(7.24) 



37 



