Expanding cos(ne + rvli) we get 

 CO 



s yj i|) j COS Y\ (|> COS [^ cos (j)) (Lf> 



-siN-niv U*Nn(ti cosCz COS (|)H^ , 



-T1-HJ 



We have (tt - i|;) - (-tt -i|j) = Zir so that the integrands are over 2Tr 

 allowing us to write the above as 



COS 



n ^j ( cos T) $ cos(z cos ^) 

 — SiNni|)jsiN >i ^ cos(i cos <>) A0 . 



-ir 



From Ryzhik and Gradshteyn (1965 - page 402) we have (since sine is odd 

 and cosine is even) the result 



fcos(v»e)Cos(icosCe- vM^ 

 = cos^r)H3[^'« cos(^\ J^(Z>J . 



(5.10) 



In a similar way we get 

 .IT 



\cos(y)e) sin(i cos (e-i|»)')4e 

 -If 



= cos n4)[at1 SlN^J^) J[,(H-)J J (5.11) 



22 



