DLMF:15.8.E19 (Q5076)

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Language	Label	Description	Also known as
English	DLMF:15.8.E19	No description defined

Statements

Defining formula

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

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DLMF:15.8.E19

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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.m2ahdec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1acdec

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Defining formula

{\displaystyle{\displaystyle z}}

C15.S1.XMD3.m1rdec

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Defining formula

{\displaystyle{\displaystyle a}}

C15.S1.XMD4.m1qdec

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Defining formula

{\displaystyle{\displaystyle c}}

C15.S1.XMD6.m1jdec

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