August 22nd, 2003, 01:09 PM

power series development
Hallo
I have got a mathematical problem.
I want to approximate an exponential function with a taylor polynom.
1+x+x^2/2+x^3/6+...+x^n/n!+....
Depending on the intervall of my value x i need to have a certain amount of polynoms for my approximation. I have found a table with a degree of polynoms that correspond with a specific intervall of x. With this table it is possible to obtain an exponential approximation of 10 digits behind the komma....
x degree of Polynom
0.05 5
0.1 6
0.2 8
0.5 10
1 13
2 17
5 25
10 36
The question i have is not mathematically easy to solve.
Can somebody show me the mathematical derivation of this table ?
Thank you !!!
August 22nd, 2003, 04:24 PM

i would imagine the table was derived by calculating terms of the taylor series / maclaurin series until the (total of the outstanding) terms become insignificant.
on the other hand there may be a direct calculation of the remainder series (ie the terms from n+1 to infinity) that if you need a proper mathematical derivation.
for what it's worth i make the last two 28 and 43 in excel (not 25 and 36)
edit: i think your table is accurate to ten significant digits rather than ten digits after the comma as you say.
Last edited by epl; August 22nd, 2003 at 04:28 PM.