202 MATHEMATICAL FORMULAE AND ELLIPTIC FUNCTIONS 



9.181 



00 



1. cos (x sin 6) = J (x) + 2/ J J 2 k(x) cos 2k6, 



CO 



2. sin (x sin 6) = 2^/2^+1 (x) sin (2k + 1)6. 



9.182 



n V^ ( n + ik) (n + k - i) ! 

 = 2/~ ~l! J 



9.183 



00 



io g | - ^ + 1) } j (x) +2 



k = I 



r / M * ^ / ^fc ^(" 

 - / W log - -V (- .) ^ T 



^ = o _,..-,_ (see 6.61) 



9.200 The differential equation: 



d?y 2 dy / 2 n(n + 



with the substitution: 



z = 3>V#> IJLX = p 



becomes: 



z = o 



which is Bessel's equation of order n + - 



2 



9.201 Two independent solutions are: 



2 = /1H-(P). 



The former remains finite for p = o; the latter becomes infinite for p = o. 



