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 certain
 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