OF UNRESTRICTED DEGREE, ORDER, AND ARGUMENT. 
4G7 
hence the expression for Q„ w (/x) becomes 
n(a+m)n[ m n 2 
Q.-W=- r W-(/t S “irsin^ 1 r.-F 
t e (m_ ' /l) T 
n 
77 + 777 
2 / 
/n 4- 77i + l m — n . 
i - i 
A 
f m — n — l\ 
e {m ~ n h 
in — n 
4/r, \i no - /u 
b-pur ~ 1 Y cos—— 7 r 
n(7i+7?i+i)n(--) 
\ 2 ] frn — 71 + 1 777 + 77 +2 
n 
71 + 771 + 1 
>!+ (24). 
The known transformation 
gives us 
and 
also 
n 
n ( 2x ) _ n Gj - t) 
u(x) ~ n(-i) 
n + m) on+m 
n + m 
n 
n + 771—1 
n 
n - 
n (n + 771 + 1) _ 2n+m+1 
n 
n + in + 1 
n + m 
n 
2 
nl ~2 
m — n — 2 
'n + 2 — m\ 
7 r cosec (- 7 r 
n 
71—771 
n 
777 — 77 — 1 
7 r cosec 
77 — 777 + 1 
7T 
n 
77 — 7/7 — 1 
hence the formula (24) may be written 
n 
Q7( j a)=- t d_J 2 
77 + m + ^n(-x) 
/ 
n 
77 — 777 
2) 
(/x 2 — 1 )*“ F 
1 t-, /77 + 777 + 1 777 — 77 
TT / —:-1--1 
2 2 2 > 
nfflBH) 
+e ! "-">? 2" - n ~ l) 1 ’ ^ {- 
777 — 77 + 1 777 + 77 + 2 
-3- 
9 9 
3 2 
5 2’ p 
(25). 
15. Next suppose the real part of /x is negative, the path of integration in the 
formula for Q/"(/x) may then be placed os in the figure, in which the line joining 
C and /x passes through the point t — 0. At C the phase of t — /x is — (£77 — 6), and 
3 o 2 
