DLMF:13.2.E8 (Q4298): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:13.2.E8	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle U\left(a,a+n+1,z\right)=\frac{(-1)^{n}{\left(1-a-% n\right)_{n}}}{z^{a+n}}M\left(-n,1-a-n,z\right)=z^{-a}\sum_{s=0}^{n}\genfrac{(% }{)}{0.0pt}{}{n}{s}{\left(a\right)_{s}}z^{-s}.}}

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DLMF:13.2.E8

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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.m2addec

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Kummer confluent hypergeometric function

Defining formula

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

C13.S2.E6.m2abdec

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Defining formula

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

C5.S2.SS3.m1addec

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Defining formula

{\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}

C1.S2.SS1.m1aadec

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Defining formula

{\displaystyle{\displaystyle n}}

C13.S1.XMD2.m1bdec

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