DLMF:15.5.E9 (Q5026)

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Language	Label	Description	Also known as
English	DLMF:15.5.E9	No description defined

Statements

Defining formula

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

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DLMF:15.5.E9

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

C5.S2.SS3.m1agdec

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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.m2ahdec

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