DLMF:1.14.E46 (Q538): Difference between revisions

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Revision as of 16:27, 1 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint ← Older edit		Latest revision as of 16:27, 1 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
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		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.m2atdec
		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.m1aaidec
		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.m2aldec
		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.m2akdec
		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.m3aafdec
		Property / Symbols used
			Q10897
		Property / Symbols used: Q10897 / rank
			Normal rank
		Property / Symbols used: Q10897 / qualifier
			Defining formula: ${\displaystyle{\displaystyle\operatorname{sign}\NVar{x}}}$ \sign@@{\NVar{x}}
		Property / Symbols used: Q10897 / qualifier
			xml-id: introduction.Sx4.p2.t1.r18.m6adec

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Latest revision as of 16:27, 1 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:1.14.E46	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}\mathcal{H}\mskip-3.0mu f\mskip 3.0mu \left(u\right)e^{iux}\mathrm{d}u=-\mathrm{i}(\operatorname{sign}x)\mathscr{F}\mskip-3.0mu f\mskip 3.0mu \left(x\right),}}$

0 references

DLMF id

DLMF:1.14.E46

0 references

Symbols used

Fourier transform

Defining formula

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

xml-id

C1.S14.E1.m2aadec

0 references

Q10895

Defining formula

${\displaystyle{\displaystyle\mathcal{H}\left(\NVar{f}\right)\left(\NVar{x}\right)}}$

xml-id

C1.S14.SS5.p1.m2aedec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2atdec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1aaidec

0 references

base of natural logarithm

Defining formula

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

xml-id

C4.S2.E11.m2aldec

0 references

imaginary unit

Defining formula

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

xml-id

C1.S9.E1.m2akdec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3aafdec

0 references

Q10897

Defining formula

${\displaystyle{\displaystyle\operatorname{sign}\NVar{x}}}$

xml-id

introduction.Sx4.p2.t1.r18.m6adec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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