Forums: » Register « |  Free Tools |  User CP |  Games |  Calendar |  Members |  FAQs |  Sitemap |  Support |

New Free Tools on Dev Shed!

#1
August 22nd, 2003, 01:09 PM
 jack37a
Junior Member

Join Date: Apr 2003
Posts: 2
Time spent in forums: < 1 sec
Reputation Power: 0
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 !!!

#2
August 22nd, 2003, 04:24 PM
 epl
Contributing User

Join Date: Mar 2001
Location: Dublin
Posts: 413
Time spent in forums: 2 h 18 m 18 sec
Reputation Power: 13
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.

 Viewing: Dev Shed Forums > Programming Languages - More > Software Design > power series development