36 DR GUSTAVE PLARR ON THE 



y —y the same as in the first case. Thus we have the slightly different expression 



We transform Q (,) and Q (r) by the help of 



a i+v>i+i - a */+i( a + iyi+i = a »/+i( a _|_ w y/+i ; 

 from which 



(a + iy»l+* = a'"/+i x fa+ 2?i y+1 • 



v ' a tl+1 



In the case of Q (r) , we put 



w = r — u , 

 and in the numerator, 



a=r+s+\— v . 

 Hence 



a+w = 2r+s+% — u — v 



—n+^—u—v, 

 because of n - s = 2r . 



Thus the numerator in Q (,,) will be 



[T + 8 + i V) X {r + s+ ^_ v y l+1 ■ 



The denominator in Q ( ' v will be 



( s+u _ v+ i)r-«/+i x yz. ; (. . 



v ' (s+u— v +iy i+i 



Dividing the first of these expressions by the second, and putting 



r _ (r+s + i-vy- u '+ 1 



(s+u-v+iy- v i+ 1 ' 



(n + i-u-vy+\s+u-v+iy + 1 

 V ~^ x ( r+g+ j_ v y/+i( r+s+ i_ t ,y/+i • 



we get 



In the case of Q (,) we put 



w = r — u 



a = r'+s+f — v. 

 Then 



a+w = 2r'+s+% — u— v=n+\— u— v , 



because of 2r' = n — 1 — s. We have then in putting 



w r . (n + l-u-vy+\*+u-v+i y^ 

 V - ^ x (y + 8 + 1 _ v )*/+i( r ' +8 + 1- v)*/ +1 ' 



