34 Mr. W. Steadman Aldis. On the Numerical 



m = 00 m = 00 



Jo(^) = f^,- ft., + 13^ -13,+ = 2 ^4.«+2 (7), 



7)1 = m = 



7)1 = 00 m = 00 



VI =0 m = 



Thus the elements ft, used in the computation of lo{x) and for 

 any vahie of x can be easily used to derive the values of Jo(a;) and 



4. We have further 



•a.(.o^j.(.0(E-iog.)-(|^^^^^ } 



also 0=^J^-l+\m-M,^M,- } 



^ ln(i)|2 n(2)|^ n(3)|- J 



whence by addition 



Oo{x) = Jo(a;){E + l-loga^} + {74-76 + 78- }-l .-.(9), 



using the notation of the former paper. 

 Again, 



G,{x) = Ji(.i-)(E-Iog..) + l 



H2 n(i)n(2) n(r)n(r + i) "^"•J 



12 n(i)n(2)^ ^n(7).n(r+i)^ i' 



whence, adding, 



G,(..) = J,(.;){E + l-log4 + l-| 



2ri(f)fl(2) 2n(r)n(r+l) 



(i^)^(Si + S,-2) _ (l^f(Si-l) - & 



2n(l)IT(2) ~ n(l)n(2) ■^8\2/ 



But 



2n(7-)ii(7 + 1) ~ "n(r)n(f + 1) "^2{n(?-+ 1)}^ 



