PROCEEDINGS 



OF THE 



Camkitrg* |){ril0S0pIjial Stfrittg, 



On the product J m (x) J n (x). By W. M c F. Orr, M.A. 



[Read May 15, 1899.] 



If in Bessel's equation we change x into ix it becomes 



d 2 u 1 du / ?i 2 \ 

 dx 2 x dx \ x 2 ) 



Writing u — x~% . v this assumes its normal form 



— - (i w 2 -l/4\ _ 



dx 2 \ x 2 J 



Replacing n by m we obtain another similar equation 



d?w__(-. w 2 -l/4\ 

 dx 2 v x 2 ) 



The product vw of any two solutions of the equations 



d 2 v T 



d 2 w T , 

 da? +IW=0 



satisfies the equation 



D ^ + »(f + r)V +y j(z+r^ + (/ _ _ p)y _ (1) 



VOL. X. PT. III. 8 



