DLMF:15.12.E2 (Q5162)

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No description defined

Language	Label	Description	Also known as
English	DLMF:15.12.E2	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle F\left(a,b;c;z\right)=\sum_{s=0}^{m-1}\frac{{% \left(a\right)_{s}}{\left(b\right)_{s}}}{{\left(c\right)_{s}}s!}z^{s}+O\left(c% ^{-m}\right),}}

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DLMF:15.12.E2

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{\displaystyle{\displaystyle|c|\to\infty}}

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order not exceeding

Defining formula

{\displaystyle{\displaystyle O\left(\NVar{x}\right)}}

C2.S1.E3.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.m2adec

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Defining formula

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

C5.S2.SS3.m1adec

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Defining formula

{\displaystyle{\displaystyle!}}

introduction.Sx4.p1.t1.r15.m5adec

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Defining formula

{\displaystyle{\displaystyle s}}

C15.S1.XMD11.m1dec

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Defining formula

{\displaystyle{\displaystyle z}}

C15.S1.XMD3.m1adec

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Defining formula

{\displaystyle{\displaystyle a}}

C15.S1.XMD4.m1dec

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Defining formula

{\displaystyle{\displaystyle b}}

C15.S1.XMD5.m1dec

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Defining formula

{\displaystyle{\displaystyle c}}

C15.S1.XMD6.m1dec

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Defining formula

{\displaystyle{\displaystyle m}}

C15.S1.XMD9.m1dec

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