208 MATHEMATICAL FORMULAE AND ELLIPTIC FUNCTIONS 



I d \ n COS X 



00 



- i) ,_ 



[ ^ _ 2n } (3 _ 2W ) . . . . 

 = o 



9.245 The general solution of 9.240 may be written: 



\*Ae ix + Be~ ix 



y = (xdx 



9.246 Another particular solution of 9.240 is: 



f ( \- . T ) 4. (^ - i)( + i) (n + 2) 



= ^ 1 ' ~ 2 



2-4-6 . . . . 2w(*V) n 



9.247 The functions \l/ n (x), ^f n (x),f n (x) satisfy the same recurrence formula^ 



9.260 The differential equation: 

 with the change of variable: 



y = u\/X 



is transformed into BesseFs equation of order n + -. 



9.261 Solutions of 9.260 are: 



i. SJ*\ = \fT. - -"' * <*V sm * 



COS 



9.262 The functions S n (x), C n (x), E n (x) satisfy the same recurrence formula 



dS n (x) n + i , x P f x 

 i. j = r&M ~ S n+l (x). 



