SEMAINE D'ÉTUDE SUR LE ROLE DE L’ANALYSE ECONOMETRIQUE ETC. 007 
Representation of an Amortization Law ¢(0) by a Taylor Series 
Expansion 
It is clear that for a given interval of variation of 0, for 
example 
.00 years 
it 1s always possible to represent any function (0) given b) 
the statistical analysis with a sufficient degree * - “roxim-"‘on 
by taking a limited number p of the terms y. T5" ex 
pansion of 3(8)e*’. Thus it is essential to study * “<-+>ties 
of this expansion. 
Expressions for ©. and 
512. Developing the different terms oi , 
have 
ul Series 
, WE 
(512-1) 
(') This is legitimate if U/1<1, a condition which is usually met by 
observed values of i—p. According to (510-8) we have u=1/T and 7 
is given below by (512-584 We will see that in any case we have T<E 
‘relation (513-2)1 
1 
Allais - pag. 211