Power expansion of the Dirac Delta function?

[andresordonez]

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.

 

[mathman]

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.

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]

Thanks