Formula:631

Digital Library of Mathematical Functions ID 1.17.E2

${\displaystyle{\displaystyle\int_{-\infty}^{\infty}\delta\left(x-a\right)\phi(x)\mathrm{d}x=\phi(a),}}$

Constraint(s)

${\displaystyle{\displaystyle a\in\mathbb{R}}}$

Symbols List

• ${\displaystyle{\displaystyle\delta\left(\NVar{x-a}\right)}}$:
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\in}}$:
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\mathbb{R}}}$:
• ${\displaystyle{\displaystyle\phi(x)}}$: continuous function
 

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