- #1
dane502
- 21
- 0
Homework Statement
Prove that the series [tex]\sum_{n=0}^\infty e^{-n^2x^2}[/tex] converges uniformly on the set [tex]\mathbb{R}\backslash\ \big] -\epsilon,\epsilon\big[[/tex] where [tex]\epsilon>0[/tex]
Homework Equations
n/a
The Attempt at a Solution
I have tried using Weierstrass M-test but I have not been able to find a suitable series.
As my topic implies I thought I could use some a series of a bell-curve like function, which I have some experience with from a probability course.
But I have a problem finding a suitable expression - let alone showing that this series convergence.
I would appreciate if someone could help getting me started (preferably without solving the entire exercise).