Power expansion of the Dirac Delta function?

  • #1
Hi, I hope this is the right place to ask this

Is it possible to expand the Dirac delta function in a power series?

[tex] \delta(x)=\sum a_n x^n [/tex]

If so, what's the radius of convergence or how can I find it?

Thanks.
 

Answers and Replies

  • #2
mathman
Science Advisor
7,956
498
Hi, I hope this is the right place to ask this

Is it possible to expand the Dirac delta function in a power series?

[tex] \delta(x)=\sum a_n x^n [/tex]

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.
 
  • #3
Thanks
 

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