DLMF:15.8.E20 (Q5077)

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Language	Label	Description	Also known as
English	DLMF:15.8.E20	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle F\left({a,1-a\atop c};z\right)=(1-z)^{c-1}F\left(% {\frac{1}{2}(c-a),\frac{1}{2}(a+c-1)\atop c};4z(1-z)\right),}}

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DLMF:15.8.E20

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{\displaystyle{\displaystyle\Re z<\frac{1}{2}}}

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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.m2aidec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1addec

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Defining formula

{\displaystyle{\displaystyle z}}

C15.S1.XMD3.m1sdec

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Defining formula

{\displaystyle{\displaystyle a}}

C15.S1.XMD4.m1rdec

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Defining formula

{\displaystyle{\displaystyle c}}

C15.S1.XMD6.m1kdec

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