DLMF:15.8.E7 (Q5064): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:15.8.E7	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle F\left({-m,b\atop c};z\right)=\frac{(c-b)_{m}}{(c% )_{m}}F\left({-m,b\atop b-c-m+1};1-z\right)=\frac{(c-b)_{m}}{(c)_{m}}z^{m}F% \left({-m,1-c-m\atop b-c-m+1};1-\frac{1}{z}\right),}}

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DLMF:15.8.E7

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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.m2aadec

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Defining formula

{\displaystyle{\displaystyle z}}

C15.S1.XMD3.m1fdec

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Defining formula

{\displaystyle{\displaystyle b}}

C15.S1.XMD5.m1fdec

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Defining formula

{\displaystyle{\displaystyle c}}

C15.S1.XMD6.m1fdec

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Defining formula

{\displaystyle{\displaystyle m}}

C15.S1.XMD9.m1adec

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