DLMF:15.5.E3 (Q5020)

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Language	Label	Description	Also known as
English	DLMF:15.5.E3	No description defined

Statements

Defining formula

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

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DLMF:15.5.E3

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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.m2abdec

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Defining formula

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

C5.S2.SS3.m1aadec

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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.m2abdec

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Defining formula

{\displaystyle{\displaystyle n}}

C15.S1.XMD10.m1adec

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Defining formula

{\displaystyle{\displaystyle z}}

C15.S1.XMD3.m1bdec

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Defining formula

{\displaystyle{\displaystyle a}}

C15.S1.XMD4.m1bdec

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Defining formula

{\displaystyle{\displaystyle b}}

C15.S1.XMD5.m1bdec

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Defining formula

{\displaystyle{\displaystyle c}}

C15.S1.XMD6.m1bdec

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