RADIATION CHARACTERISTICS OF AN ANTENNA. 



233 



n+ 1 



1- 



A^ 



-,+ 



3 (7? + 3) 5-3 (n + 3) (« + 5) 

 A^ 



7-o-3(« + 3) (« + o)(» + 7) 



+ 



In like manner 



(102) 



/i = 



2A 



j J _ {2Ay ^ {2Ay 



2(n+l)| 3(n + 3) ' 5-3 (?i + 3) (ri+ 5) 



7-5-3(n + 3)(» + 5)(n+7)^ f . 



Now taking up integral 1-2 from equation (99), let us write it 





d(t) sin" d cos 6 



\ 1 — cos {;2A cos 6) ( 



I 2 



and expanding cos (2 A cos d) in series, obtain 



h 



P 



= ^/rf0[sin" 



, \ {2 AY cos2 (2a)* cos'' 9 , 

 cos -^ -^-^^ ^ -J + 



(103) 



I 



This equation, integrated in Gamma Functions between the limits 

 and ^72 gives 



'^ = 2 



{2Ay 



r fn + 1 

 2 



r(2; 



2 



'■ 2r^4--^+i 



r(3) 



(Ml! 



4! 2rf- + 5 



\ 2 



+ 1 



+ 



2A^ 



(n+l)(n+3) 



1 - 



2A' 



-^ + 



2.4* 



3(n + 5) 5-3(w+5)(w+7) 



(104) 



Employing the values of /i, /o, ^s found in equations (103), (104) 

 and (102) we may write the expression for the mutual power in the 

 integrated form 



