I'm taking Advanced Mathematics Physics without having any previous experience in physics, which is fine since my math is advanced enough. However I got stock on this problem. I'm not asking you guys to do my homework, just maybe some help to get me going and finishing this problem, that so far is the only one I can't do.
I have to prove by induction that:
Integral from negative infinity to infinity of [(dm/dxm)( δ(x))(f(x))] = (-1)m fm(0)
Now I know that:
δ(x-a) = 0 when x isn't equals to a
the integral of δ(x-a)dx = 1
and the integral of f(x) δ(x-a)dx = f(a)
but I'm a little confused...I think it might be me overthinking the problem, or just not being familiar with this sort of problem.
I'm new to the forums and it might be a lot of me to ask for help without previously posting anything, but I'll do my best to help others in problems I do know.
I attached a picture if that helps