﻿326 Dr. I, J. Schwatt on the 



Adding by columns we have 

 i iM ^.=M 1 , 1 +(M 1 , 2 +M 2 , 2 ) + ... + (M 1> K + M 2 , K + ...+M K , K ) 



a=l P=a 



j8=l a=l 



tc + l\(/c + l — «\ d*u K+1 -P 



u" 



By means of (4) the form (3) changes to 



s -i<-»'i(- i ''("- 1 X*l«*)- *. 

 =I,(-)'»'^'i,<-«f: 1 )(*Ji:")- 



Now 



/*4-l\/* + l-a\ (a; -I- 1)1 (g + !-«)! 0! 



V a A £-« /-(« + !-«)!»!• (iB + l^IOS-a)!^! 



~(* + l-/3)!/S!V-<0l"l \ # A«/ 

 Therefore 



b " 1 f(-i)-(f).i(-i)-(f)-i-(i-D«-i— i, 



and (5) becomes 



ln u K+l-fJ 



dx n 

 Hence 



d n u K+1 * . _ ft / /c + 1 \ d V +1 



d#" 



= ,5o ( - 1) ( p r-d*-> mQ »— ^^ =0 ' 



and A K+1 is of the same form as the one assumed for A K in 



(2). 



II. The following is another method for proving the 

 given theorem. 



