544 THE ELECTROMAGNETIC FIELD. [PT. III. CH. XIII. 



from which follows the reduction-formula 



20-1 



(21) = T 



Integrating (19) again by parts, writing the integrand 



sin 



IT IT 



cos 2 <? +1 v sin^-V / 2 2w - 1 P 



7T/ - - * * + / - COS 2 U+V y SU1 2 (p-1) 



2<7 + l ' _E 20 + 1 J A 



(22) 



,. ,, - , - , 



giving the reduction-formula, 



By q successive applications of the reduction-formula (21) and p 

 of the formula (23) we get 



^ 



But we have 



Accordingly, introducing even factors into numerator and 

 denominator, 



and our integral (17) becomes 



* 



(26) I (ft - 2 



7y( ' - 



If we multiply this by ^yr = lT375_72^T) ' the series 



-' ! (2?)P - ( " 1)g 



