DLMF:13.3.E19 (Q4353)

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Language	Label	Description	Also known as
English	DLMF:13.3.E19	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\left(z\frac{\mathrm{d}}{\mathrm{d}z}z\right)^{n}% \left(z^{b-a-1}e^{-z}M\left(a,b,z\right)\right)={\left(b-a\right)_{n}}z^{b-a+n% -1}e^{-z}M\left(a-n,b,z\right),}}

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DLMF:13.3.E19

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$$={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$$ Kummer confluent hypergeometric function

Defining formula

{\displaystyle{\displaystyle M\left(\NVar{a},\NVar{b},\NVar{z}\right)}}

C13.S2.E2.m2akdec

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Defining formula

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

C5.S2.SS3.m1acdec

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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.m2addec

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base of natural logarithm

Defining formula

{\displaystyle{\displaystyle\mathrm{e}}}

C4.S2.E11.m2adec

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Defining formula

{\displaystyle{\displaystyle n}}

C13.S1.XMD2.m1cdec

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Defining formula

{\displaystyle{\displaystyle z}}

C13.S1.XMD6.m1rdec

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