Taylor Series

[matiz]

Hi,

I understand the Taylor series expansion for f(x) which is defined (at a) as below

f(a) + f'(a) (x-a)/1! + f''(a)(x-a)^2/2! ....

What is the Taylor series representation of f(x + delta(x)) and how is it arrived at? I am trying to understand the derivation of continuous compounding rate of interest calculation.

Thanks for your help

 

[bigbadwolf]

f(x + delta(x)) = f(x) + f '(x)(delta(x))/1! + f ''(x)(delta(x)^2/2! + ...

A triviality -- just replacing x with x + (delta(x)), a with x, and (x-a) with delta(x).

 

[matiz]

ok, thanks