Formula:811

Digital Library of Mathematical Functions ID 2.6.E16

${\displaystyle{\displaystyle\left\langle f_{n},\phi\right\rangle=(-1)^{n}\int_{0}^{\infty}f_{n,n}(t)\phi^{(n)}(t)\mathrm{d}t,}}$

Constraint(s)

${\displaystyle{\displaystyle\phi\in\mathcal{T}}}$

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
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle\mathcal{T}}}$: space of decreasing functions
• ${\displaystyle{\displaystyle f_{n,n}(t)}}$: n th repeated integral
 

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