DLMF:1.16.E38 (Q646)

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Language	Label	Description	Also known as
English	DLMF:1.16.E38	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\left\langle\mathscr{F}\left(\delta\right),\phi% \right\rangle=\left\langle\delta,\mathscr{F}(\phi)\right\rangle=\left\langle% \delta,\frac{1}{\sqrt{2\pi}}\int^{\infty}_{-\infty}\phi(t){\mathrm{e}^{\mathrm% {i}xt}}\mathrm{d}t\right\rangle=\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}% \phi(t)\mathrm{d}t=\frac{1}{\sqrt{2\pi}}\left\langle 1,\phi\right\rangle,}}

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DLMF:1.16.E38

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

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2acdec

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Defining formula

{\displaystyle{\displaystyle\delta_{x}}}

C1.S16.SS3.m1afdec

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Defining formula

{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

C1.S4.SS4.m1afdec

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Defining formula

{\displaystyle{\displaystyle\left\langle\NVar{\Lambda},\NVar{\phi}\right% \rangle}}

C1.S16.SS1.p5.m5apdec

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Fourier transform of a tempered distribution

Defining formula

{\displaystyle{\displaystyle\mathscr{F}\left(\NVar{u}\right)}}

C1.S16.E35.m2acdec

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Defining formula

{\displaystyle{\displaystyle\in}}

introduction.Sx4.p1.t1.r10.m2ahdec

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Sitelinks

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