RADIATION CHARACTERISTICS OF AN ANTENNA. 



223 



Note that 



and 



^r- 



n 



w+ 1 



= 2 



2 • 4 • 6 • • • ?i — 2 

 1-3-5- • -n — 1 



Vi 



r,^+. 



w + 3 



= 2 



2-4'6' • -n 

 1-3-5---W+ 1 



(74) 



(75) 



Putting these values in equation (71) we obtain 



P=--I(-l)^-, 



m 



-i + 



sin^fi 



n ' 2(7^+1) 



"^ '''^^^ w r 2 (w + 1) ^ 2!22 (71 + 1) (n + 3) 



£« 



+ 5 sin 5 



3!23(w+ 1) (n + 3) (w+5) 



1 j 1 _ £2 1 



w I n + 1 2 (n + 1) (n + 3) 

 B^ 1 



+ ■ 



+ 



2^2 (w + 1) (w + 3) (71 + 5) 

 1 



B^ 



2^3 {n + 1) (71 + 3) (71 + 5) (71 + 7) 



+ 



where 



71 = 2, 4, 6, . . . 



U' 



(76) 



Equation (76) may be further improved for purposes of calculation 

 by expanding the trigonometric functions in power series and col- 

 lecting the terms. For this purpose 



2^ 



8! 



+ 



', (77) 



