RADIATION CHARACTERISTICS OF A\ ANTENNA. 



233 



?i+ 1 



1 - 



A^ 





3(n+3) 5-3 (/i+ 3) (n + 5) 

 7-5-3(7i + 3) (w + f)) {ji + 7) 



+ 



(102) 



In like manner 



h 



2A 



\ ^ (2Ay ^ ^ {2Ay 



2 (w + 1) ) 'S{n-\- 3) ' 5-3 (n + 3) (n + 5) 



i2AY 



-^ + 



I 



r 



7-5-3(n + 3) (71 + 5) (w + 7) 



Now taking up integral I2 from equation (99), let us write it 



r-/2 ^ . ^ ^ M - COS (2zl cos 0) / 

 " = / d<t> sm" cos d j — ^ ^ , 



(103) 



\ 2 



and expanding cos (2 A cos 6) in series, obtain 



h= ^ f d(f>\ sin" d cos ^ - 



\ {2 AY cos'^ 9 _ (2a)'* cos^ g , ^ 



2! 4: '^ ( 



This equation, integrated in Gamma Functions between the limits 

 and 7r/2 gives 



I2 = 



2 



/(^r(2) 



(2^) 



"■ 2rr'^+i 



2 



r(3) 



^= 2rr^^ + i 



+ 



2^2 



(n+l)(n+3) 



1- 



2A' 



_,2A' 



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



(104) 



Emplojang the values of /i, h, I^ found in equations (103), (104) 

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

 integrated form 



