DLMF:18.26.E19 (Q5949)

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Language	Label	Description	Also known as
English	DLMF:18.26.E19	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle(1-z)^{-c+iy}{{}_{2}F_{1}}\left({a+iy,b+iy\atop a+% b};z\right)=\sum_{n=0}^{\infty}\frac{S_{n}\left(y^{2};a,b,c\right)}{{\left(a+b% \right)_{n}}n!}z^{n},}}

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DLMF:18.26.E19

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{\displaystyle{\displaystyle|z|<1}}

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Defining formula

{\displaystyle{\displaystyle{{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};% \NVar{z}\right)}}

C16.S2.m5aadec

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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 S_{\NVar{n}}\left(\NVar{x};\NVar{a},\NVar{b},% \NVar{c}\right)}}

C18.S25.T1.t1.r3.m2addec

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Defining formula

{\displaystyle{\displaystyle!}}

introduction.Sx4.p1.t1.r15.m5addec

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Defining formula

{\displaystyle{\displaystyle\mathrm{i}}}

C1.S9.E1.m2afdec

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Defining formula

{\displaystyle{\displaystyle y}}

C18.S1.XMD1.m1idec

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Defining formula

{\displaystyle{\displaystyle z}}

C18.S1.XMD2.m1adec

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Defining formula

{\displaystyle{\displaystyle n}}

C18.S1.XMD6.m1qdec

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