Qg Art. 4. —M. Kuniyeda : 



whence 



(83) p a{n, i^ + 1 ) + qAa(n, p + q + ^) = (n + l) a{n + 1, p) 



(h = 0,1,'2, ). 



Hence 



(84) a{n, p + q + A) = ^^^ a[n +\,p)- y^- a{n, p + l). 



For instance, take the case 



0<q<\, o.= l + f^)— . 



Then, Ijy (SO), we have 



Widere ^={^^^'' ^- = (1 + ,),--'«^^^ 



are independent of n and p. 

 Let us suppose that 



p<q, 



so tliat 1+/? < 1 + g, 



and we have 



whence 



We have also 



Hence we have 



(n + 1 ) «(■». + 1 , i?) > a{ih p+V. 



Thus we obtain, hy (84), 



ain,p + q + '\) ^ . {n+\) a(n+\,p) . 



qA 



