Symbols:Greek/Delta/Dirac Delta Function

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:

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

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

Sources

• 1978: Ronald N. Bracewell: The Fourier Transform and its Applications (2nd ed.) ... (previous) ... (next): Frontispiece
• 1978: Ronald N. Bracewell: The Fourier Transform and its Applications (2nd ed.) ... (previous) ... (next): Chapter $4$: Notation for some useful Functions: Summary of special symbols: Table $4.1$ Special symbols
• 1978: Ronald N. Bracewell: The Fourier Transform and its Applications (2nd ed.) ... (previous) ... (next): Inside Back Cover
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Appendix $1$: Symbols and Conventions: Greek Alphabet
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): $\map \delta x$