28 DR GUSTAVE PLARR ON THE 



By the general type we have 



IL(a+x) = Ilax(a + iyi+ 1 



Applying these, we get 



W" = AT, 

 where 



( - l) v U(2 n - 2v)Jl(u - v)2 2v 1 



~ 2" + s+2u IL;IIO - v)VL{n - s - 2u) X II(s+u-- v)ll(u- v) X 'IL(u- v) ' 



( -l)«(2n+l-2v) 8ff+1 .(u-v+l) w/+1 .2- 2< 



2V{n-v + iyi+ 1 



v 1 i- 1 .(n-s-2w)W- 1 



(s+u-v+iy+*+\u-v+iyi+ i .v<+ 1 .v'+\u-v+iyi+ i ' 



Reducing A, we have 



(-l) u U(2n-2v)2- n - s - 2 "+ 2v 



Uvll(n - v)IL(n -s- 2u)II(s + u— v)H.(u - v) ' 

 As to T we extract from it a factor Q depending onj> only, taking 



(s + U-V + l) i+J l +1 = (8 + U-V + iyi+ 1 X(s + U-V+j + l) i l+ l , 



and having by this relation if we make s = — 



(u-v+iy+jt+ i , . ,..._ 



(u — t> + iy /+1 v > J i / 



and putting 



T = Q(j)xP(i,j), 

 we have 



Q0V <»-.-»"-« 



'2*'(s + w—y + l>« +1 .y/+ 1 ' 



( - iy . (2m. + 1 - 2v) 2i '+\u -v+j + iyi +1 .2- 2i 

 "^'3)— ^_«±iw+i x .'c 



D*7-i 



(» - v + 1)' 7+1 (a + u - v +j + iy+\it - v + 1 )*/+il«'/+i 



We may further transform P(?', j) by applying the general formulas 



a»i- 1 = (-lf.(-ayi+ l 

 2a? b '+ 1 = 2a b '+ 2 x (2a + l) s */+ 2 

 = 2 26 .a 6 /+ 1 (a+D 6/+1 



Thus 



These give 

 Also, applying 



(-l)V/- 1 =(-v)"+ 1 



(2w + I - 2w)*'+ I = 2 2 ' . («, + 1 - vy+\7t + 1 - vy+ l 



( - yyz+i^ + \ - v yi+i( u . -v+j + i y/+ * 



a 26/-l = 2 W. a i/-I( a _l)fc/-l 



-2 (-ay/+ , (-tt+|)* /+1 , 



