DLMF:15.12.E3 (Q5163)

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Language	Label	Description	Also known as
English	DLMF:15.12.E3	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle F\left({a,b\atop c+\lambda};z\right)\sim\frac{% \Gamma\left(c+\lambda\right)}{\Gamma\left(c-b+\lambda\right)}\sum_{s=0}^{% \infty}q_{s}(z){\left(b\right)_{s}}\lambda^{-s-b},}}

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DLMF:15.12.E3

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Defining formula

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

C5.S2.E1.m2adec

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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.m2aadec

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Defining formula

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

C5.S2.SS3.m1aadec

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Defining formula

{\displaystyle{\displaystyle\sim}}

C2.S1.SS3.p1.m11adec

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Defining formula

{\displaystyle{\displaystyle s}}

C15.S1.XMD11.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.m1adec

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Defining formula

{\displaystyle{\displaystyle b}}

C15.S1.XMD5.m1adec

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Defining formula

{\displaystyle{\displaystyle c}}

C15.S1.XMD6.m1adec

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Defining formula

{\displaystyle{\displaystyle q_{s}(z)}}

C15.S12.XMD2.m1dec

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