( 634 ) 
or that we assume 
7p 
ne ae 
For a finite g and sin @ not approaching to naught, we can always 
have a series (XIII), converging in the point x with a mark, giving 
perhaps a very small but yet certainly .a finite difference with unity. 
The demonstration would not hold goed for =z, that is for negative 
real « Meanwhile in order that in a certain point «the series may 
converge with the marks w, it is no necessity that one of the 
circles of fig. 9 includes the point; it suffices if # lies im G' and 
as now the boundary of G', cuts the real axis on the left side of 
«=O at a distance 
1 
en 
log 2 
it is clear that also for negative but finite « there are series (XIII) 
which converge with a mark decidedly smaller than unity. 
’ 
Suppose we have «=—1, we then find from 
l 
A 
e= |, 
log 2 
. . . 1 
that the series (XIV) converges still just with the mark — for 
1 han : 
UZ, c= — — in the point r=—1. By verification we find 
2 log 2 ; 
1 
<= 1—0.718740.3407—0.1752 + 0.0861— 0.0439 +0.0216—0.0107+4. 
The quotient of the successive terms is already immediately fairly 
ik 
equal to — and the sum of the calculated terms is 0.5009. 
If we now pass to the development of an arbitrary function / (2) 
on the ground of the development XIII we have but a slight diffe- 
rence to bring about in the reasoning. For u point «= ge! the 
successive values 
7p 
uj—=l—e vj | sin Gaj) | 
have to be calculated when 6—2; differs from 2. Should 4 become 
equal to a; the value w; must be replaced by 
41-2” “ 
