240 

 For: 



; / 



ƒ' 



<p'\ («)z=/ = — j 'Ix j x„ (.«) d.v = — .r j ■/„(a-)ci .r -|- L- /„ («) rf* = . 







If we should deduce the function rf\ (.v) from y), f.r\ in the manner 

 which Voi.TEKRA indicates, the second and third derivates of <p, {x) 

 would not be zero at the point x = I. Therefore we define the 

 function 



r ru—s)' 

 X. W = -[] ^YT ^" ^'^ * + ^' -^ +^. 







Ci and Z>i being constantvS determinated by 



I 



1 Xi («) da; = 







In this waj, the second and third derivates of •/, (•^') <ake at the 

 points X = and .c= / the prescribed values; on ihe other hand 

 fore-fold integration of /, (.r) gives rise to a function, the second 

 and third derivates of which are at the point .t = /also equal to zero. 



This being staled, we are lead to define the series of functions 



X. i-^) = q' + c> -^ + D, 



X, (^) = - [ ƒ ^^^ X. («) ds + 6', X + D^ 







X, (*•) = - [ ƒ ^r X. (*) d, + C,x + D,^ 







r r(x—sy i 



Xn («) = — • I 3, X»-i (») <^ + C„.r + -i^" 







where the coefficients d and Di are bound bj' the conditions 



Cxi (x) dx=0 







I 

 I Xj- (a;) . a: (fiK ^ 

 



