DLMF:13.13.E5 (Q4482)

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Language	Label	Description	Also known as
English	DLMF:13.13.E5	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle e^{y}\left(\frac{x}{x+y}\right)^{b-a}\sum_{n=0}^{% \infty}\frac{{\left(b-a\right)_{n}}y^{n}}{n!(x+y)^{n}}\*M\left(a-n,b,x\right),}}

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DLMF:13.13.E5

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{\displaystyle{\displaystyle\Re((y+x)/x)>\frac{1}{2}}}

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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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Defining formula

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

C5.S2.SS3.m1addec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2aadec

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Defining formula

{\displaystyle{\displaystyle!}}

introduction.Sx4.p1.t1.r15.m5addec

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Defining formula

{\displaystyle{\displaystyle n}}

C13.S1.XMD2.m1ddec

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Defining formula

{\displaystyle{\displaystyle x}}

C13.S1.XMD4.m1ddec

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Defining formula

{\displaystyle{\displaystyle y}}

C13.S1.XMD5.m1ddec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1aadec

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