Can one get the Taylor series for e^-(t^2)?

[nomadreid]

Trying to get the MacLauren series expansion for f(t) = exp(-t²), I get the ridiculous result that f(t) = 1. Trying to get the Taylor series for this function by setting a = 1 doesn't seem to produce a meaningful result either. How can I get an expansion for this function? Or is there a condition for the Taylor series expansion that this function is not fulfilling?

 

[tkhunny]

Try \(\displaystyle f(t) = e^{t}\),

Then try \(\displaystyle g(t) = e^{-t}\)

Then think about \(\displaystyle h(t) = e^{-t^{2}}\)

When we have Uniform Convergence, many things can happen.