34 DR GUSTAVE PLAHR ON THE 



If in the second member we put under the sign F, 



a + /3-y+l = e, 

 e = y', 



and expressing 

 we get 

 Now 



F (20) by (ii.), 



*\ y',e' J y'/-"/ +1 \a + B-y' + l,e'J 



e'-S'=--a + l3 + S-y-e + l = £; 



We have thus (III.) 



mi\ v( a >P> B ) (y-p-*'+\e-/3)-"<+* / «,/U x 



(111) *Vy,eA 7 -a/+i e -a/+i " r ^ a + | g_ y + 1)a + / 8_ e + 1 j 



with the above signification of £. 



In our application of this we shall find £=0, in consequence of which the F of the 

 second member will reduce itself to its first term, which is unity. 



§ iv. 



We apply (II.) to the transformation of 



Ki]p(»,i) of §n. 



We have to put 

 This gives 



Then 

 where 



«= —v, {3 = n+^ — v, S = u—v+j + l 

 y = u — v + 1, € = s+8. 



— a= +v 

 y-ft=u+$-n 

 e — S = S. 

 a+fi—y+l=n+^—u—v 



(u-v+iy +l 



. ; ( - v yi+\ (n + b- v) il+l . s t7+1 



ry t >3)-lii+\( n + l_ u _ v yi+i( s + u _ v+ j + : iyi+i 



