Function of any Number of Variates. 451 



It will thus he required to show that 



A 7-,. J 7 . ( 7 . - L2SSpjX^X 7 +2Stt;»A» 



_ ^—^SSrpqWpWq /^ 



The evaluation of this integral will be possible i£ the 

 exponent — gg SSSpjAyX, + ffiw^Xp is reduced to the form 



- 2g SSSp^Xp + «p)(Xg + oj) + 9ft 2SS ll2 «y« 2 and the in- 

 tegral (1) is then equal to 



2S SS P?*p*<i 



Thus it remains only to show that 

 Putting i\p=Xp' and iu p =* p \ we have 



= M S2S M (V + V) (V + <V) - i S2S M «/«/ 



Hence we have 





This is a system of linear equation, to determine tin 

 ilifterent u t . 

 Putting 



A = ^ • A , - ^ A 



3 S 



the solution is 



a$ = A 7^"">- 



1 2 



