Register to reply

Error terms in Taylor Series

by Nurdan
Tags: error, series, taylor, terms
Share this thread:
Nurdan
#1
Dec16-08, 02:43 PM
P: 4
It is known that
[tex] \sum\limits_{k = 0}^\infty {\frac{{N^k }}{{k!}}} = e^N[/tex]


I am looking for any asymptotic approximation which gives

[tex] \sum\limits_{k = 0}^M {\frac{{N^k }}{{k!}}} = ? [/tex]
where [tex]M\leq N[/tex] an integer.


This is not an homework
Phys.Org News Partner Science news on Phys.org
Hoverbike drone project for air transport takes off
Earlier Stone Age artifacts found in Northern Cape of South Africa
Study reveals new characteristics of complex oxide surfaces
christianjb
#2
Dec16-08, 09:18 PM
P: 529
I'm only being a little facetious if I point out that the sum is asymptotically equal to e^N.

Want more accuracy? It's better approximated by e^N-[x^(N+1)]/(N+1)!


Register to reply

Related Discussions
Error in Taylor polynomial of e^x Calculus & Beyond Homework 4
Taylor Polynomial Error-Please help! Calculus & Beyond Homework 2
Really need help - Taylor Polynomial Approximation Error Calculus & Beyond Homework 2
Regression: MLEs when error terms are not identically distributed Calculus & Beyond Homework 0
Taylor Expansion and Error Calculus & Beyond Homework 1