DLMF:13.2.E5 (Q4295): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:13.2.E5	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\lim_{b\to-n}\frac{M\left(a,b,z\right)}{\Gamma% \left(b\right)}={\mathbf{M}}\left(a,-n,z\right)=\frac{{\left(a\right)_{n+1}}}{% (n+1)!}z^{n+1}M\left(a+n+1,n+2,z\right).}}

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DLMF:13.2.E5

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Defining formula

{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

C5.S2.E1.m2abdec

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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.m2abdec

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Olver’s confluent hypergeometric function

Defining formula

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

C13.S2.E3.m2abdec

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Defining formula

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

C5.S2.SS3.m1abdec

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Defining formula

{\displaystyle{\displaystyle!}}

introduction.Sx4.p1.t1.r15.m5abdec

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Defining formula

{\displaystyle{\displaystyle n}}

C13.S1.XMD2.m1dec

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Defining formula

{\displaystyle{\displaystyle z}}

C13.S1.XMD6.m1ddec

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