Encyclopedia > Talk:Taylor series

  Article Content

Talk:Taylor series

"Note that there are examples of infinitely often differentiable functions f(x) whose Taylor series converge but are not equal to f(x). For instance, all the derivatives of f(x) = exp(-1/x²) are zero at x = 0, so the Taylor series of f(x) is zero, and its radius of convergence is infinite, even though the function most definitely is not zero."

f(x) has no Taylor series for a=0, since f(0) is not defined. You have to state explicitly that you've defined f(x)=exp(-1/x²) for x not equal to 0 and f(0)=0 . This is merely lim[x->0] f(x), but it is a requirement for rigor.

Don't complain, fix! Wikipedia:Be bold in editing pages. -- Tim Starling 02:03 16 Jun 2003 (UTC)



All Wikipedia text is available under the terms of the GNU Free Documentation License

 
  Search Encyclopedia

Search over one million articles, find something about almost anything!
 
 
  
  Featured Article
Kings Park, New York

... with no husband present, and 23.4% are non-families. 20.1% of all households are made up of individuals and 10.6% have someone living alone who is 65 years of age ...

 
 
 
This page was created in 1685 ms