Symbols:Greek/Delta/Dirac Delta Function

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Dirac Delta Function

$\map \delta x$

Let $\epsilon \in \R_{>0}$ be a (strictly) positive real number.

Consider the real function $F_\epsilon: \R \to \R$ defined as:

$\map {F_\epsilon} x := \begin{cases} 0 & : x < 0 \\ \dfrac 1 \epsilon & : 0 \le x \le \epsilon \\ 0 & : x > \epsilon \end{cases}$

The Dirac delta function is defined as:

$\map \delta x := \displaystyle \lim_{\epsilon \mathop \to 0} \map {F_\epsilon} x$

The $\LaTeX$ code for \(\map \delta x\) is \map \delta x .