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

From DRMF

Jump to navigation Jump to search

← Older edit

Revision as of 16:39, 1 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 16:39, 1 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
(2 intermediate revisions by the same user not shown)
		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

---

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)

Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q646&oldid=23755"