( 304 ) 
structed as follows. Each of the points a=Aet determines a curve 
whose equation written in polar coordinates is 
Ap 
a cos p (O—/3) ’ 
and the totality of these curves divides the z-plane into a system of 
curvilinear polygons. In one of these polygons, which we shall 
designate by Gp», the origin and the circle of convergence of the 
DD 
series 2c, 2” are contained. We suppose now that the point z never 
0 
leaves the interior of this polygon Gj. 
In that case we constantly have 
POD < oa 
and consequently 
real part of (5 br) >? 
In other words, we may affirm that the points t in the «-plane 
are situated outside the circle with diameter 1 + ¢ and centre 
x= —4(1-+<). Moreover, since necessarily we must suppose || 
to remain finite, there is a non-evanescent minimum value of |t], 
so that it must be possible to draw the loop W in such a manner, 
that all the points ¢ remain outside, the loop thereby enclosing 
at the same time the circle with diameter 1 and centre «= — }. 
The latter condition is imposed on the path W in order that 
during the integration we shall constantly have 
real part of Ee +1) > 0. 
With the thus constructed loop W as path of integration the 
equation 
a 
en cr ge ip 5 = = ; 
DAG) ee neue je fe ze ) de 
W 
retains its signification, even when the point < passes beyond the 
circle of convergence, if only it remains within Gj. 
= 
dak et 
