DLMF:5.12.E12 (Q2157): Difference between revisions

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Revision as of 13:13, 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 01:03, 2 January 2020 Admin (talk | contribs) Bureaucrats, Interface administrators, Administrators 57,118 edits ‎Changed an Item: Add constraint
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		Property / Symbols used
			beta function
		Property / Symbols used: beta function / rank
			Normal rank
		Property / Symbols used: beta function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{B}\left(\NVar{a},\NVar{b}\right)}}$ \EulerBeta@{\NVar{a}}{\NVar{b}}
		Property / Symbols used: beta function / qualifier
			xml-id: C5.S12.E1.m2akdec
		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.m2ahdec
		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.m1akdec
		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.m2abdec
		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.m3akdec
		Property / Symbols used
			sine function
		Property / Symbols used: sine function / rank
			Normal rank
		Property / Symbols used: sine function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\sin\NVar{z}}}$ \sin@@{\NVar{z}}
		Property / Symbols used: sine function / qualifier
			xml-id: C4.S14.E1.m2acdec
		Property / Symbols used
			Q11275
		Property / Symbols used: Q11275 / rank
			Normal rank
		Property / Symbols used: Q11275 / qualifier
			Defining formula: ${\displaystyle{\displaystyle a}}$ a
		Property / Symbols used: Q11275 / qualifier
			xml-id: C5.S1.XMD8.m1kdec
		Property / Symbols used
			Q11283
		Property / Symbols used: Q11283 / rank
			Normal rank
		Property / Symbols used: Q11283 / qualifier
			Defining formula: ${\displaystyle{\displaystyle b}}$ b
		Property / Symbols used: Q11283 / qualifier
			xml-id: C5.S1.XMD9.m1kdec
		Property / Symbols used
			Q11291
		Property / Symbols used: Q11291 / rank
			Normal rank
		Property / Symbols used: Q11291 / qualifier
			Defining formula: ${\displaystyle{\displaystyle P}}$ P
		Property / Symbols used: Q11291 / qualifier
			xml-id: C5.S12.XMD1.m1dec

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Latest revision as of 01:03, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:5.12.E12	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\int_{P}^{(1+,0+,1-,0-)}t^{a-1}(1-t)^{b-1}\mathrm{d}t=-4e^{\pi i(a+b)}\sin\left(\pi a\right)\sin\left(\pi b\right)\mathrm{B}\left(a,b\right),}}$

0 references

DLMF id

DLMF:5.12.E12

0 references

Symbols used

beta function

Defining formula

${\displaystyle{\displaystyle\mathrm{B}\left(\NVar{a},\NVar{b}\right)}}$

xml-id

C5.S12.E1.m2akdec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2ahdec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1akdec

0 references

base of natural logarithm

Defining formula

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

xml-id

C4.S2.E11.m2abdec

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.m3akdec

0 references

sine function

Defining formula

${\displaystyle{\displaystyle\sin\NVar{z}}}$

xml-id

C4.S14.E1.m2acdec

0 references

Q11275

Defining formula

${\displaystyle{\displaystyle a}}$

xml-id

C5.S1.XMD8.m1kdec

0 references

Q11283

Defining formula

${\displaystyle{\displaystyle b}}$

xml-id

C5.S1.XMD9.m1kdec

0 references

Q11291

Defining formula

${\displaystyle{\displaystyle P}}$

xml-id

C5.S12.XMD1.m1dec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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