293 



= h [Ci>-{-lJ'-l,> + C/,_l_.2/,,^,_(_, -]- 0/,^_,3/-2/,-f2 + • . .] 



thus 



o 



Substituting tliis value in the equation (13) we see that ff{.v) may 

 be expressed in differential coefticients of the function /(.v) and two 

 integrals. To determine the law of the coefficients A^^/'), .4//'), /J (/'j, 

 At^P^' . . . we put together the values for /> = 'L 2, . . . 10 in tlie 

 following table : 



Examining this table we see that 



A,'p) = A,(/'-^' + A,(p-^) 



If therefore the coefticients of order p — 2 and p — 1 are known 

 those of order /; may be found. To verify ihe results we may 

 remark that if 



2A/p) = Si, 

 we must find 



The resulting values of these coefticients are as follow? 



20 

 Proceedings Royal Acad. Amsterdam. Vol. XMI. 



