and further 
dyn (a) = ad (mot 2) ors wee, 
if a is a certain positive constant. The value of a, is here equal 
to a, consequently constant, and we have 
Baa a. 
Let us consider, in the neighbourhood of «=O, a function wu of 
the form 
== +(1- Jot — )|- een 
u c E= By 7g B 41) ( ) 
in which c and y are positive constant values which are at our 
disposal. However we may dispose of them, the function « always 
belongs to 8) and its maximum modulus J/ (8), on the circumference 
of (3), satisfies the condition 
MAGA) 2605 “Sih ace Se 
For from the development of w in a power series 
ln A 53 eB 
=(intast | Gaal) 
which has merely positive coefficients, follows that w attains its maxi- 
mum modulus on the circumference of (8) for & =p, and in that 
point the form between brackets in the righthand member of (17) 
is smaller than 1. For the transmuted function of wu, in the point 
2a we now find after some calculation 
Tula Me oct 
n (841) 
or, if we take n <1 
c 
Jh —__-— 19 
u («) = n@ai) (19) 
There now exists a certain positive number t such that there is 
corresponding to any arbitrarily given small number d a function u, 
belonging to (3), and for which the conditions 
M (8)<.d and | Lu(e)| it 
are at the same time satisfied. 
For, according to (18, and (19) we need only take in (17) 
J 
(6+1)r 
if the latter amount is smaller than 1, and else for some 
proper fraction. The condition of continuity, occurring in the propo- 
sition of N°. 11, is therefore not satisfied in the whole domain (a), 
and we observe moreover that for t even an arbitrarily great 
number may be taken. 
Gi, I= 
