# Dirac delta function

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The Dirac delta function, \( \delta (x) \) can be loosely defined as the function \[\delta(x) = \begin{cases} + \infty ,\quad x = 0 \\ 0 ,\: \qquad x \ne 1 \end{cases} \] and it satisfy the equation \( \displaystyle \int_{-\infty}^{\infty} \delta(x) \, dx = 1 \).

\[ \large \displaystyle\int _{ -\infty }^{ \infty }{ { e }^{ -{ x }^{ 2 } }\delta ({ x }^{ 2 }-2)\quad \, dx } =\dfrac { A{ e }^{ -B } }{ C\sqrt [ D ]{ F } } \]

The equation above holds true for positive integers \(A,B,C,D\) and \(F\), find the minimum value of \(A+B+C+D+F+2\).

**Notation**: \(\delta(\cdot)\) denotes the Dirac delta function.

**Cite as:**Dirac delta function.

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