The Dirac delta function cannot be expanded into a power series due to its non-analytic nature. Specifically, a function can only be represented by a power series in a neighborhood of zero if it is analytic there, which the Dirac delta function is not. This conclusion is supported by mathematical definitions that classify the delta function as not being a conventional function.
PREREQUISITESMathematicians, physicists, and students studying advanced calculus or functional analysis who seek to understand the limitations of the Dirac delta function in mathematical representations.
No. A function can be represented by a power series in a neighborhood of 0 only if it is analytic there. The delta function is not analytic. It is (from a mathematics point of view) not even a function.andresordonez said:Hi, I hope this is the right place to ask this
Is it possible to expand the Dirac delta function in a power series?
\delta(x)=\sum a_n x^n
If so, what's the radius of convergence or how can I find it?
Thanks.