1256 
If now we expand the function 
o ZP 
g (ce) =e-* J bn, —=—e *X 
Dr ae 
in a power series, we have, differentiating 7 times, and putting 
d 
D a= 
de 
ge) (x) — Pr (e= X) — p-« (D + 1)() 4 
—=e-* > (—1)p Gi D—p) X 
0 
where 
CA are uP 
DO X= 3 boty 
which, for the value «= 0, gives 
D,®) oe 
Introducing this value, we obtain 
iL n z n an 
JO = (DP bey 6," = (Ip ECD Gp =H 5 
Sp An 
g(e) = = (—1)" — a 
0 n! 
and finally 
ende 
a 
(n!)? 
This solution agrees with that of Le Roy. In his memoir the 
discussion of this formula for different values of a, may be found. 
f(y) = {1,(2V2y) = (1 
0 
Mathematics. — ‘Some remarks on the coherence type 4.” By 
Prof. L. E. J. Brouwer. 
In order to introduce the notion of a “coherence type’ we shall 
say that a set M is normally connected, if to some sequences f of 
elements of M are adjoined certain elements of M as their “limiting 
elements”, the following conditions being satisfied : 
1st. each limiting element of f is at the same time a limiting 
element of each end segment of /. 
2nd, for each limiting element of f a partial sequence of f can 
be found of which it is the on/y limiting element. 
3. each limiting element of a partial sequence of f is at the 
same time a limiting element of f. 
4. if m is the only limiting element of the sequence {m,} and 
