H. E. 80PER, A. W. Young, B. M. Cave, A. Lee, K. Pearson 335 
n-l^ w+1 2 ^1.2.(ri+l)(« + 3) 4 
^ 1 . 2 . 3 . («, + 1) (n + 3) (w + 5) 8 ^ ■■ 
(xx)bis, 
and again for p = 2 
^P'^ ^ {n + I) {n - 1)^ ^ ' [ ^ », + 3 2 1 . 2 (» + 3) + 6) 4 
1 . 2 . 3 + 3) (« + 5) {n + 7) 8 ■"■} 
The series in (xx) and (xxi) for = 25 and upwards converge with sufficient 
rapidity to determine /^a' and p.^ rapidly and therefore with accurate values for 
jLt^' and ft../ will give ju-j oi' ^'^d ix^, and thus provide the determination of jSj. 
We will now determine ^-'2^+1 in like manner. We have 
;/ - 1 
but 
_ . 1^.2.-2 _ 1) ,,2.-4 , y(y- l )(lJ-2) _ 
(™ 2! 3! 
+ (- 1)^ (1 - . 
XT ' _ ' y (y - 1) ' , y (y - 1) (y - 2 ) , 
tlence ^ 2})+i J*/^ 23)-i 2I P' 3 ! 2P-.5 
- + (- ^rX2p+i (xxii), 
where 
n - 1 
n - 4: + 2p 
11-2+ 2« 
_ (i-p2) 2 1 r+i (Z"-2£7 , , _ ,2. — ^r-'. 
77 (« - 3) ! - 2 + 2^9 j _i (r/3)«-2 ^ ^ ' 
or integrating by parts 
= MWlZ r (1 - r'f-i^' dr 
77 (« - 3) ! (n - 2 + 2j)) ,1 ' (f (i-/))"-' 
