KiRSTiNE Smith 
25 
Evaluating this by (24) and (25) we get 
V+l^r, s 
1 \r+s 
(p-2)2(p- l)P-2''"'-i' 
X [ip^Pp^i^ s-l • jSj,-!, r-1 • p+1 n . ptl r, .9 + ^3), s-1 • ^ V, r-1 ■ n p+i, • „+i H p+i, J ... (31 ). 
But 
?T ^jy+l. v+1 ■ ^r. j>+l • ^.f, p+1 
r, s — p+l'-'-r, .9 
I>+1 
V+l^'-V+l-r ~ p+l'-'-r,!! 
c 
p+1 ^r. i 
and 
p+1 
n = - "-ti 
3)+i n s 3? 
--ji+i, p+1 
Substituting these values in (31) we find 
,+lA,, = (-l)'■+^l''-^2''-^..(]^-2)2(^,-l)}2/2^'<''-l^,i3,_l,,_,.^,_l,,_l.^y^.^^^ 
4 
(p- s + 1) (jQ-r+ 1) e-r, , . e 
p+1. p+1. 
I 
1 
and as the last fraction equals 
^r, p+1 '^s, D+1 
p+iK,s={-'^y'-'i^p,.^-i-^p,r-i{i''-'.^''-'---{p-^)Hp~w-^'''''-'\+A^ 
with which the proof bv induction for (25) is carried through. 
(8) We shall now return to (23). It consists of 2p + 1 terms of which the 
(2r -!- l)st originally was found as {^rcrl — 2,-1 cr^) so that 
^ 2r - 1 
1 ! 
^ 2r + 1 
a" 
N 
1 
1 
1 
1 
2r + 1 2r + 3 
1 
4r — 1 
2r - 1 2r + 1 
2r - 1 
_1 
2r + 1 
1 
4r - 3 
1 
1 
1 
2r + 1 
1 
27T3 
1 
2r + 1 2r + 3 4r + 1 
