DLMF:1.16.E38 (Q646): Difference between revisions

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Revision as of 12:23, 29 December 2019 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Created a new Item: Wikidata Toolkit example test item creation		Latest revision as of 16:39, 1 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
(12 intermediate revisions by the same user not shown)
		Property / constraint
			${\displaystyle{\displaystyle\phi\in\mathcal{T}}}$ \phi\in\mathcal{T}
		Property / constraint: ${\displaystyle{\displaystyle\phi\in\mathcal{T}}}$ / rank
			Normal rank
		Property / Symbols used
			the ratio of the circumference of a circle to its diameter
		Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
			Normal rank
		Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
			Defining formula: ${\displaystyle{\displaystyle\pi}}$ \cpi
		Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
			xml-id: C3.S12.E1.m2acdec
		Property / Symbols used
			Q10908
		Property / Symbols used: Q10908 / rank
			Normal rank
		Property / Symbols used: Q10908 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\delta_{x}}}$ \deltaDistribution[x]
		Property / Symbols used: Q10908 / qualifier
			xml-id: C1.S16.SS3.m1afdec
		Property / Symbols used
			Q10770
		Property / Symbols used: Q10770 / rank
			Normal rank
		Property / Symbols used: Q10770 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$ \diff{\NVar{x}}
		Property / Symbols used: Q10770 / qualifier
			xml-id: C1.S4.SS4.m1afdec
		Property / Symbols used
			Q10905
		Property / Symbols used: Q10905 / rank
			Normal rank
		Property / Symbols used: Q10905 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\left\langle\NVar{\Lambda},\NVar{\phi}\right\rangle}}$ \intinnerprod{\NVar{\Lambda}}{\NVar{\phi}}
		Property / Symbols used: Q10905 / qualifier
			xml-id: C1.S16.SS1.p5.m5apdec
		Property / Symbols used
			Fourier transform of a tempered distribution
		Property / Symbols used: Fourier transform of a tempered distribution / rank
			Normal rank
		Property / Symbols used: Fourier transform of a tempered distribution / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathscr{F}\left(\NVar{u}\right)}}$ \Fouriertransdist@{\NVar{u}}
		Property / Symbols used: Fourier transform of a tempered distribution / qualifier
			xml-id: C1.S16.E35.m2acdec
		Property / Symbols used
			Q10784
		Property / Symbols used: Q10784 / rank
			Normal rank
		Property / Symbols used: Q10784 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\in}}$ \in
		Property / Symbols used: Q10784 / qualifier
			xml-id: introduction.Sx4.p1.t1.r10.m2ahdec
		Property / Symbols used
			base of natural logarithm
		Property / Symbols used: base of natural logarithm / rank
			Normal rank
		Property / Symbols used: base of natural logarithm / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{e}}}$ \expe
		Property / Symbols used: base of natural logarithm / qualifier
			xml-id: C4.S2.E11.m2acdec
		Property / Symbols used
			imaginary unit
		Property / Symbols used: imaginary unit / rank
			Normal rank
		Property / Symbols used: imaginary unit / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{i}}}$ \iunit
		Property / Symbols used: imaginary unit / qualifier
			xml-id: C1.S9.E1.m2aedec
		Property / Symbols used
			Q10771
		Property / Symbols used: Q10771 / rank
			Normal rank
		Property / Symbols used: Q10771 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\int}}$ \int
		Property / Symbols used: Q10771 / qualifier
			xml-id: C1.S4.SS4.m3afdec
		Property / Symbols used
			Q10914
		Property / Symbols used: Q10914 / rank
			Normal rank
		Property / Symbols used: Q10914 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathcal{T}}}$ \mathcal{T}
		Property / Symbols used: Q10914 / qualifier
			xml-id: C1.S16.XMD12.m1adec
		Property / Symbols used
			Fourier transform of a test function (locally)
		Property / Symbols used: Fourier transform of a test function (locally) / rank
			Normal rank
		Property / Symbols used: Fourier transform of a test function (locally) / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathscr{F}(\phi)}}$ \mathscr{F}(\phi)
		Property / Symbols used: Fourier transform of a test function (locally) / qualifier
			xml-id: C1.S16.XMD15.m1ddec
		Property / Symbols used
			Q10910
		Property / Symbols used: Q10910 / rank
			Normal rank
		Property / Symbols used: Q10910 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\phi(x)}}$ \phi(x)
		Property / Symbols used: Q10910 / qualifier
			xml-id: C1.S16.XMD7.m1bdec

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Latest revision as of 16:39, 1 January 2020

No description defined

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

Statements

Defining formula

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

0 references

DLMF id

DLMF:1.16.E38

0 references

constraint

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

0 references

Symbols used

the ratio of the circumference of a circle to its diameter

Defining formula

${\displaystyle{\displaystyle\pi}}$

xml-id

C3.S12.E1.m2acdec

0 references

Q10908

Defining formula

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

xml-id

C1.S16.SS3.m1afdec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1afdec

0 references

Q10905

Defining formula

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

xml-id

C1.S16.SS1.p5.m5apdec

0 references

Fourier transform of a tempered distribution

Defining formula

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

xml-id

C1.S16.E35.m2acdec

0 references

Q10784

Defining formula

${\displaystyle{\displaystyle\in}}$

xml-id

introduction.Sx4.p1.t1.r10.m2ahdec

0 references

base of natural logarithm

Defining formula

${\displaystyle{\displaystyle\mathrm{e}}}$

xml-id

C4.S2.E11.m2acdec

0 references

imaginary unit

Defining formula

${\displaystyle{\displaystyle\mathrm{i}}}$

xml-id

C1.S9.E1.m2aedec

0 references

Q10771

Defining formula

${\displaystyle{\displaystyle\int}}$

xml-id

C1.S4.SS4.m3afdec

0 references

Q10914

Defining formula

${\displaystyle{\displaystyle\mathcal{T}}}$

xml-id

C1.S16.XMD12.m1adec

0 references

Fourier transform of a test function (locally)

Defining formula

${\displaystyle{\displaystyle\mathscr{F}(\phi)}}$

xml-id

C1.S16.XMD15.m1ddec

0 references

Q10910

Defining formula

${\displaystyle{\displaystyle\phi(x)}}$

xml-id

C1.S16.XMD7.m1bdec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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