DLMF:15.5.E6 (Q5023)

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Language	Label	Description	Also known as
English	DLMF:15.5.E6	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}\left((1% -z)^{a+b-c}F\left(a,b;c;z\right)\right)=\frac{{\left(c-a\right)_{n}}{\left(c-b% \right)_{n}}}{{\left(c\right)_{n}}}(1-z)^{a+b-c-n}\*F\left(a,b;c+n;z\right).}}

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DLMF:15.5.E6

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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.m2aedec

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Defining formula

{\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}

C5.S2.SS3.m1addec

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derivative of $$f$$ with respect to $$x$$

Defining formula

{\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}

C1.S4.E4.m2aedec

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Defining formula

{\displaystyle{\displaystyle n}}

C15.S1.XMD10.m1ddec

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Defining formula

{\displaystyle{\displaystyle z}}

C15.S1.XMD3.m1edec

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Defining formula

{\displaystyle{\displaystyle a}}

C15.S1.XMD4.m1edec

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Defining formula

{\displaystyle{\displaystyle b}}

C15.S1.XMD5.m1edec

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