1903-4.] Solution of the Differential Equation of 
273 
[n] * 
The Complete Solution of the Differential Equation of 
J [n] . By the Rev. P. H. Jackson, H.M.S. “Irresistible.” 
Communicated by Dr Wm. Peddie. 
(MS. received April 23, 1904. Read July 4, 1904.) 
In connection with the function J^j, it may he of interest 
to give briefly the complete solution of the differential equation 
satisfied by the function J [ri ] . The method of Frobenius will be 
employed. Consider the differential equation 
pxff {l -[»]-[- n] }x ll] / a \x) 
+ X A J~ (x p ) 4- [n\ [ - n\ f(x) = 0 . . . (a) 
in which 
If jp= 1, the equation reduces to 
x 2 ^ + x jf + ( x 2 - n 2 ) f = 0 , 
which is Bessel’s equation for functions of order n . 
Substituting an expression 
/(*>- 2 ^ [ ° +s) 
in the equation (a) , we have an indicial equation 
[a + ?z] [a - w] = 0 , 
PROC. ROY. SOC. EDIN, — VOL. XXV. 
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