(71 ) 



2\ = 



^ 



öF, 



q \....p 



q=p^l 



where 



u—p 



dWg 



u—\ 



V-F -^- a.,-„ 



U—\ 



+ sign for 0.^12.. (u-l) {u + l) ... p)={q I ... p)) 



dXl2...;, 



So 



T — V* V ^'^912...(m-1Xm-H). ..p 



f — sign for (j/^ 12 ...((/ — !)(?< 4-1) ..;>) = (^ 1 ...jo) J 



q—u 



■^^ 0''Xl2...;, 



The second derivative supplies the terms 



^'="2-* d^. 



«=1 

 f+ sign for (u 12 ...(w-l)(u f 1) ...;>)=: (12 .. p) 



r for (qn I. ..{u-\){ui-l)...p)^(q 12. ..p)\ 



or 



, r, 'V^ ÖA^12.. («-!)(«+ 0...;, 



where ^i2...(h— i)(m+i).../) = T. a ^ 



9=/'+ 1 

 dXl2...;, 



9=/'-^ 1 



^^' (- sign for (n 12 ... (?^-l) (« + 1) ... ;)) = (12 ...p)] . 



u=p q=H 



g^ j7 _ V^ '^ Ö'X^12..(u-l)(«+l)..;t, 



u = 1 9 = ^) -|- 1 



d^'ud^'^ 



( — sign for {qui . . {u — l){u-{'l)..p) r=: {ql2 ..p)\ 



u = p 



'^ 0'Xi2.. 



tt=l 



