382 Mr. L. Isserlis : Application of Solid Hyper geometrical 

 Thus Y = cc'F 1 = cc'22A s , s - say, 



p'tt Y = Cc'%Xks, s'(s+l)Xs' + 1)W. 



Let F(«, a', & % *, */) = 2£A SS . a-/ 



= %oo> 

 and letx*,*' = ^'Xoo> 



7S 7s 



where 0(w) = ^— {xu) and <fi(u) — ^- (yw) , 



so that 



6 t (l> t '{xy) = {s+iy(s' + iyxy. . . . (3) 



We have then 



y 

 F i= (7Cao) x=9=1 = —t 

 : and 



p' tt ,Y = cc'.c i c' v ( X t,t>)x=y=v 



P 



'* = *!?*(&*) (4) 



V %oo 7^=1 v ; 



^ 00 satisfies the differential equations (1) and (2) . 

 Similarly ^=Xoi-%oo, 



Solving these equations, we find 



^ 2 §^=X2o-3%io+2xoo, 



.3-« 



2, 



005 



W §^ =Xo2 - 3%oi + 2^00. 



Multiply equations (1) and (2) by se, y respectively after 

 writing m 1 = a + ^, m 1 / = a / + /5 J m 2 = a/3, m 2 ' = «p, and 

 noting that 7 — a — «' — /3— l = n. 



