40 DR GUST AVE PLARR ON THE 



We have 



Hence 

 Also from 



2r' = n — 1 — s 

 r' + l+s — n-r'. 



tt) , , ~ = (r' + l+s-v). 



Ii(r +s— v) K ' 



2n-2r' = n + l+s 

 1 111 



U(n+l+a-2v) (v+l+s-2v) U(n+s-2v) 2r'+2 + 2s-2v IL(n+s-2v)' 



and 



1 2 2 " _ 2x2 2 " 



C)2/-2u 9«— 1— s 2" —s ' 



We have by these 



r , TL (2n-2'u-2v)I[(8+u-v) 2 2 " 



where 



( r , + l+8-v)x2 



0l -(2r'+2 + 2s-2t;) = UDlt ^ 



Again C can therefore be put under the form 



C =TT x 



B 1 A 2»- i n(%+s-2t))' 



hence we have inform the equality, 



ABC = ABC, 



although, of course, n — s is even in the second member, and n—l—s is so in the 

 first. 



As to D and D', we put them at once under the form 



D= ( r y/-i.( r _ £)»/-i 





D= (7+s + i)"/- 1 (r' + «) t ' / ~ I ' 



Applying (<i) for D, and for D', 



(2a + l) 2 »/- 1 = 2 2 ''(a+£y/- 1 « ft /- , , 

 hence 



(<*+.,)' (a;/ -2 26 II(2a + l-26) 

 we get 



II(2r)II(2r+2s-2v) 



D = 



II(2r-2v)II(2r + 2s) 



1 , _ n(2 / + l)n(2r' + l + 2.s-2^) 

 ~ 1 1 ( 2V + 1 - 2v)ri(2r' + 1 + 2s) ' 



