Formula:597

Digital Library of Mathematical Functions ID 1.16.E27

${\displaystyle{\displaystyle\left\langle D^{k}f,\phi\right\rangle=(-1)^{\left|k\right|}\int_{{\mathbb{R}^{n}}}f(x)\phi^{(k)}(x)\mathrm{d}x,}}$

Constraint(s)

${\displaystyle{\displaystyle\phi\in\mathcal{D}_{n}}}$

Symbols List

• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\left\langle\NVar{\Lambda},\NVar{\phi}\right\rangle}}$:
• ${\displaystyle{\displaystyle\in}}$:
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\mathbb{R}}}$:
• ${\displaystyle{\displaystyle k}}$: integer
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle\mathcal{D}_{n}}}$: space of test functions
• ${\displaystyle{\displaystyle\phi(x_{1},x_{2},\dots,x_{n})}}$: test function
• ${\displaystyle{\displaystyle Df}}$:
 

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