DLMF:15.10.E11 (Q5127)

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Language	Label	Description	Also known as
English	DLMF:15.10.E11	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle w_{1}(z)=F\left({a,b\atop c};z\right)=(1-z)^{c-a-% b}F\left({c-a,c-b\atop c};z\right)=(1-z)^{-a}F\left({a,c-b\atop c};\frac{z}{z-% 1}\right)=(1-z)^{-b}F\left({c-a,b\atop c};\frac{z}{z-1}\right).}}

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DLMF:15.10.E11

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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.m2afdec

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Defining formula

{\displaystyle{\displaystyle z}}

C15.S1.XMD3.m1jdec

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Defining formula

{\displaystyle{\displaystyle a}}

C15.S1.XMD4.m1jdec

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Defining formula

{\displaystyle{\displaystyle b}}

C15.S1.XMD5.m1jdec

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Defining formula

{\displaystyle{\displaystyle c}}

C15.S1.XMD6.m1gdec

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Defining formula

{\displaystyle{\displaystyle w_{m}(z)}}

C15.S10.XMD2.m1dec

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