202 
PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28 
[. — THE GENERAL CASE 
8(8)e** CAN BE DEVELOPED AS A TAYLOR SERIES 
Hypothesis: The Development of B(8)e*® as a Tavlor Series 
510. Assume that the function 3(8)e*’, in which y is a cer- 
tain constant, can be developed as a Taylor series (1). This is 
a very general hypothesis. Then 
n-1 
(510-1) OBERT RL SL Pa 
n-1! 
Since 
(510-2) 
ref" u)_= [° e 2 
-/ 8le)do of == / Bele do 
we have 
(510-3) 
rab BL ms, 
u pe pe 
b 6 b 
(510- b(u J [= 00 een = 
510-4) ( ) R [nou + ms) +. aul + 
(*) It goes without saying that for practical purposes it is only of use 
to consider an interval for § of o to 25 vears. or at most of o to 100 vears. 
(3 Relations (211-3) and (220-1) 
[rr] Allais - pag. 206