( 532 ) 
For the coefficients B,,, we find 
1m a—1)* uk 1 zalk _m uk 
Bam Dimon Demo (1-5 
(a—u)k _m!\ a a 
et 
qm 
Bn, h— (m—1),-1 
So the series of polynomials (V) becomes 
== Dineke, (VD) 
za 
or af we like 
1 1 x Come sing - +2 al en: 
l—wz a i a 
The series of polynomials has again become a geometrical series 
with the ratio [1-+-a(a—l)]:a, and the region of convergence must 
be a circle. We do not pay attention to this casual circumstance, but 
we determine G, according to the general rule, according to which 
Gs is made in the z-plane the representation ot the circle unity of 
the u-plane with the aid of the relation 
a—l 
een A) 
a" 
or 
dz 1 
BR 
1 ee 
noe 
From this is evident that the region of divergence G, encloses 
that part of the z-plane which is situated outside the circle with 
1 ‘Metal EEN : i eo as : 
centre — ee and radius |— Ik The interior of this circle is the 
A LA 
region of convergence (fig. 1); on the boundary of G lies the sin- 
gular point z= 1, 
