( 741 ) 
or 
a. … as An—l 
oat i ae ait Sok Er 
D(wyi)e = 
pee An _ Set Atl 
n n+l en 4 wer 
ig Ris +- AE JA Ke} 
that the first member of this equation is independent of a,a,..d,-1- 
Thus assuming 
2 3 
| À 
D (ay) = B rj BA + E, ORE E, 3/ En ee 
and 
a, 1. Ss File — a À, + oe Inl nl 
2 9 n—l 
D(eyde == 
0 0 vt 0 a’ a 
=e — E, ri Sah prot ap bie 
we find 
ee ua ee Wee a 
Ey anne en ape ia inne ees age 
EEZ a 
that is 
Ey = (Ep) a=as=..—=a (15) 
Bsa 
Having thus established the relations (14) and (15) we may conclude 
that if 
I (a n—l 
Bef 
(w—y)* n 
the formulae for D(vyA) and D(a) where the coefficients are written 
im Press form, still hold: if 4. 4,—= -. +4, = 0. 
The same result may at once be deduced from the rule given by 
Porcaré. For if instead of the coefficients of Frrpunorm we take 
those of PremrrJ and remark that the /-fold integral of a eycle of 
k letters always gives 
b 
‘| 
a 
then it is evident that those terms from PLrEMELJ’s coefficients must 
be omitted which contain a, a,..a,—1 or what is equivalent, that in 
these coefficients must be substituted 
b 
b 
[ren K(8y).. K(ue) da...du = [Kr (aa) dee = ay, 
. 
a a 
AIEE OS ee ek ee 
