Power expansion of the Dirac Delta function?

AI Thread Summary
The Dirac delta function cannot be expanded into a power series, as it is not analytic in any neighborhood. It does not meet the criteria for representation by a power series due to its nature as a distribution rather than a conventional function. Consequently, there is no radius of convergence for such an expansion. The discussion emphasizes the mathematical distinction between functions and distributions. Understanding this difference is crucial for analyzing the properties of the Dirac delta function.
andresordonez
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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.
 
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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.
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.
 
Thanks
 

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