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

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Latest revision as of 14:03, 2 January 2020

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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).}}

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DLMF:8.17.E9

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

Defining formula

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

C15.S2.E1.m2abdec

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incomplete beta function

Defining formula

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

C8.S17.E1.m2addec

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Defining formula

{\displaystyle{\displaystyle a}}

C8.S17.XMD1.m1gdec

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Defining formula

{\displaystyle{\displaystyle b}}

C8.S17.XMD2.m1fdec

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Defining formula

{\displaystyle{\displaystyle x}}

C8.S17.XMD3.m1gdec

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