1. Mathematics
2. Calculus and Analysis
3. Real Analysis
4. Integrals
5. 16881

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Show that

is a representation of the Dirac S-function.
Discussion:
Let

and let f(x) be a function which is piecewise continuous on [?a, a], in particular,

(Dirac delta function)

one must show that

One way of doing this is to follow the approach used to obtain an analogous result in the process of establishing the validity of the Fourier series theorem, and then use the result that