204 
rM!0FERS>0?v zV. SCrrrSTER ox SOME DEFIXITE IXTEOKALS, 
hi + 1 
ip + 1) + S; (p - D) = (r. - 2) ^1%, ip) + in + 3) {p), 
2n + 1 
— 1) + - i)) -= 
.T (S; (,.> + 1) - s: (p - 1)) 
—. X '( r : 0 > + i ) + u :(;)- i )) 
’''.T’(V;(,, + i) +v;(^,-i)) 
(?t + (T + ] ) (/? — (7 + 1) ^ , 
- ^-'+1 i.p) 
>/ + 4 
0 / + cr) (rt — a) 
+ 
II — o 
s: (;>). 
(v 2 + cr -f- 1) — 1) ^ (p) 
— [n — cr) [n + 2) \-Pp\ (p), 
{n-\-a + 2){n--2}YZ\ip) 
— (n —■ cr — 1) (ii ■-{- 3) ( 2 )), 
(/i+cr +l)(/i — cr +1) , z 
(// 4- a) in - ( 7 ) 
n — 2 
{I< -l)l^UAp) + {'-‘ + i)^'U{p). 
---.F’ (u:(/> -- vtAp + 1 )) = “-t 
-I n o ii — 
(V;(,> - n - v;:(/, + i)) = (p) 
n — cr — 1 
U — .) 
S: ■ 1 (i>). 
§ 10. Xumcrical Calculations of the Four Series. 
For llie calculation of tljc nninerical values r)f the series tlie special case 
cr = 0 was taken as starting-point. Tn this particular case the well-kiunvn Integral 
+ 1 
P;iCm]j9<lp = — TTjy 
ill +p-2)ll ill - p-2) l\ 
-1 {r -H p + 1) M(/; —pi 4- 1) 1! 
which holds when 71 + is odd and n — 1, gives 
W. 
n :! + 2) 1! 
.„ 3);; P (n + ^, + 1) :: (,, _ ^ + 1) !! 
ill -F p — 2) ! 1 (n ~ p ~ 2) !! 
; when n is even and j) odd. 
The values of M° were calculated hy this equation for all values of -p up to and 
including =11, and for all values of 71 up to and including 12. The first of the 
equations K, § 9, was then applied, and substituting cr = 2, )i = 2, and Mo = 0, the 
value of Mo was calculated. Sinillarly putting 11 = 4, G, iScc., the values of Mf, for even 
values of n were all tabulated. By successive steps 1 similarly found Mf,, Mil, ‘kc., up 
