Neumann Functions G„(V) and Y n (x). C50 



and the results verified from the relation 



GrJo — G Ji= -. 



The G functions can also be calculated from the J function?, 

 and this provides another method of verification : — 

 For large values of x, 



J » w = s/h- ( PoW cos (*~ i)- Q » w sin (*- 1) } 



and 

 G (.r) = - ^/|- | P » sin (x- J)+ QoW cos (., - Vj } 



Put Qo(#) = K sin O and P (V) — P cos O . 

 Then 



tan 6 =Q (x) J P (a?) and # can be found. 



Hence 



G (^) = - ^- JuW • tan (*— "J + #o V 

 Similarly, 



g 1 (^)= + 1. JjO) . cot (<r~ \+e\ 



where tan 0i = Qi(#) / Pi(#). 



The following interpolation formulae may be used in 

 connexion with these tables, viz. : — 



n / 7n T-, W P 7i 4 f\ 3 \ -) ~ , N 



a (*±A)={i- 1± - +F4 (i-^...J.G (*) 



+ { +A+ JS ± 6( 1 -i»)-i25( 1 -i»)-}- Gl W' 



G 1 (,*^{i^4 2 ( 1 -j)4;(i-j)4;(i-| + 5)....a lW 



For comparison, it may be noted that G M (#) is the 

 same as 



~^Y» [Nielsen], -~K„(.r) [Graf u. Gutter], 



- Y„(«r) [Schafheitlin], and — T-N B (a;) [Jahnke n. Emde]. 



