Difference between revisions of "DLMF:5.12.E4 (Q2149)"

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Revision as of 11:13, 29 December 2019 Admin (talk | contribs) (‎Created a new Item: Wikidata Toolkit example test item creation)		Latest revision as of 17:44, 1 January 2020 Admin (talk | contribs) (‎Changed an Item: Add constraint)
(8 intermediate revisions by the same user not shown)
		Property / constraint
		+	${\displaystyle{\displaystyle|\operatorname{ph}z|<\pi}}$ |\phase@@{z}|<\pi
		Property / constraint: ${\displaystyle{\displaystyle|\operatorname{ph}z|<\pi}}$ / rank
		+	Normal rank
		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.m2acdec
		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.m2aadec
		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.m1acdec
		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.m3acdec
		Property / Symbols used
		+	Q10817
		Property / Symbols used: Q10817 / rank
		+	Normal rank
		Property / Symbols used: Q10817 / qualifier
		+	Defining formula: ${\displaystyle{\displaystyle\operatorname{ph}}}$ \phase
		Property / Symbols used: Q10817 / qualifier
		+	xml-id: C1.S9.E7.m1adec
		Property / Symbols used
		+	Q11273
		Property / Symbols used: Q11273 / rank
		+	Normal rank
		Property / Symbols used: Q11273 / qualifier
		+	Defining formula: ${\displaystyle{\displaystyle z}}$ z
		Property / Symbols used: Q11273 / qualifier
		+	xml-id: C5.S1.XMD7.m1dec
		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.m1cdec
		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.m1cdec

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Latest revision as of 17:44, 1 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:5.12.E4	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\int_{0}^{1}\frac{t^{a-1}(1-t)^{b-1}}{(t+z)^{a+b}}\mathrm{d}t=\mathrm{B}\left(a,b\right)(1+z)^{-a}z^{-b},}}$

0 references

DLMF id

DLMF:5.12.E4

0 references

constraint

${\displaystyle{\displaystyle|\operatorname{ph}z|<\pi}}$

0 references

Symbols used

beta function

Defining formula

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

xml-id

C5.S12.E1.m2acdec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

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

xml-id

C3.S12.E1.m2aadec

0 references

Q10770

Defining formula

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

xml-id

C1.S4.SS4.m1acdec

0 references

Q10771

Defining formula

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

xml-id

C1.S4.SS4.m3acdec

0 references

Q10817

Defining formula

${\displaystyle{\displaystyle\operatorname{ph}}}$

xml-id

C1.S9.E7.m1adec

0 references

Q11273

Defining formula

${\displaystyle{\displaystyle z}}$

xml-id

C5.S1.XMD7.m1dec

0 references

Q11275

Defining formula

${\displaystyle{\displaystyle a}}$

xml-id

C5.S1.XMD8.m1cdec

0 references

Q11283

Defining formula

${\displaystyle{\displaystyle b}}$

xml-id

C5.S1.XMD9.m1cdec

0 references

 

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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