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Dirac Delta Function: Basics


Hello Friends

I browsed some of the previous posts in this forum on Dirac Delta function, and found some interesting distributions used to represent the delta function, at the below website:

<http://mathworld.wolfram.com/DeltaFunction.html>

Also when I tried using one of the distribution, Fourier series approximation (shown below), I was getting very different solutions for different entries of upper limit of k, even at higher values of upper limits.

DeltaF(x - a) = 1/(2*Pi) + 
   (1/Pi)*Sum[Cos[k*a]*Cos[k*x] + Sin[k*a]*Sin[k*x], 
     {k, 1, Infinity}]

(here DeltaF is DiracDelta).

Does anyone here can give me suggestions on using right distributions and parameters. Thanks.

Also Can I use the DiracDelta[] function available in Mathematica itself. How does Mathematica calculate them.

I am not integrating the equation containing DiracDelta[], so as seen from the Mathematica examples, I think it is doing Laplace transformations.

Any help/directions to resources are appreciated. Thanks,

Gopinath
Graduate Student
University of Oklahoma


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