DLMF:8.17.E9 (Q2649): Difference between revisions

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Revision as of 13:29, 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 14:03, 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
			$$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function
		Property / Symbols used: $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function / rank
			Normal rank
		Property / Symbols used: $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function / qualifier
			Defining formula: ${\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}$ \hyperF@{\NVar{a}}{\NVar{b}}{\NVar{c}}{\NVar{z}}
		Property / Symbols used: $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function / qualifier
			xml-id: C15.S2.E1.m2abdec
		Property / Symbols used
			incomplete beta function
		Property / Symbols used: incomplete beta function / rank
			Normal rank
		Property / Symbols used: incomplete beta function / qualifier
			Defining formula: ${\displaystyle{\displaystyle\mathrm{B}_{\NVar{x}}\left(\NVar{a},\NVar{b}\right)}}$ \incBeta{\NVar{x}}@{\NVar{a}}{\NVar{b}}
		Property / Symbols used: incomplete beta function / qualifier
			xml-id: C8.S17.E1.m2addec
		Property / Symbols used
			Q11360
		Property / Symbols used: Q11360 / rank
			Normal rank
		Property / Symbols used: Q11360 / qualifier
			Defining formula: ${\displaystyle{\displaystyle a}}$ a
		Property / Symbols used: Q11360 / qualifier
			xml-id: C8.S17.XMD1.m1gdec
		Property / Symbols used
			Q11361
		Property / Symbols used: Q11361 / rank
			Normal rank
		Property / Symbols used: Q11361 / qualifier
			Defining formula: ${\displaystyle{\displaystyle b}}$ b
		Property / Symbols used: Q11361 / qualifier
			xml-id: C8.S17.XMD2.m1fdec
		Property / Symbols used
			Q11362
		Property / Symbols used: Q11362 / rank
			Normal rank
		Property / Symbols used: Q11362 / qualifier
			Defining formula: ${\displaystyle{\displaystyle x}}$ x
		Property / Symbols used: Q11362 / qualifier
			xml-id: C8.S17.XMD3.m1gdec

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Latest revision as of 14:03, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:8.17.E9	No description defined

Statements

Defining formula

${\displaystyle{\displaystyle\mathrm{B}_{x}\left(a,b\right)=\frac{x^{a}(1-x)^{b-1}}{a}F\left({1,1-b\atop a+1};\frac{x}{x-1}\right).}}$

0 references

DLMF id

DLMF:8.17.E9

0 references

Symbols used

$$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function

Defining formula

${\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}$

xml-id

C15.S2.E1.m2abdec

0 references

incomplete beta function

Defining formula

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

xml-id

C8.S17.E1.m2addec

0 references

Q11360

Defining formula

${\displaystyle{\displaystyle a}}$

xml-id

C8.S17.XMD1.m1gdec

0 references

Q11361

Defining formula

${\displaystyle{\displaystyle b}}$

xml-id

C8.S17.XMD2.m1fdec

0 references

Q11362

Defining formula

${\displaystyle{\displaystyle x}}$

xml-id

C8.S17.XMD3.m1gdec

0 references

 

Sitelinks

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DRMF related sites(0 entries)

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