Prove the property of Dirac's Delta

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SUMMARY

The discussion focuses on proving a property of the Dirac delta function as presented in John David Jackson's "Classical Electrodynamics." The user seeks assistance in demonstrating this property, referencing the scaling property of the delta function. The solution involves expressing a function near its zeros and utilizing the localization of the Dirac delta function to simplify the proof by omitting higher-order terms.

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Let [tex]\lbrace x_i \rbrace[/tex]be the zeroes of function f(x). Near the zeroes, you can write the function as [tex]f(x) = f'(x_i)(x-x_i) + O(x-x_i)^2.[/tex] As the Dirac delta is entirely localized at xi, you can just drop all higher order terms and it's still exact. Then you can use the scaling property of delta function, http://en.wikipedia.org/wiki/Dirac_delta_function#Scaling_and_symmetry
 
Ok. Thank you clamtrox.
 

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