DLMF:15.7.E5 (Q5055)

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Language	Label	Description	Also known as
English	DLMF:15.7.E5	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\frac{\mathbf{F}\left(a,b;c;z\right)}{\mathbf{F}% \left(a+1,b+1;c+1;z\right)}={x_{0}+\cfrac{y_{1}}{x_{1}+\cfrac{y_{2}}{x_{2}+% \cfrac{y_{3}}{x_{3}+\cdots}}}},}}

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DLMF:15.7.E5

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$$={{}_{2}{\mathbf{F}}_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Olver’s hypergeometric function

Defining formula

{\displaystyle{\displaystyle\mathbf{F}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z% }\right)}}

C15.S2.E2.m2abdec

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Defining formula

{\displaystyle{\displaystyle x}}

C15.S1.XMD1.m1dec

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Defining formula

{\displaystyle{\displaystyle y}}

C15.S1.XMD2.m1dec

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Defining formula

{\displaystyle{\displaystyle z}}

C15.S1.XMD3.m1cdec

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Defining formula

{\displaystyle{\displaystyle a}}

C15.S1.XMD4.m1ddec

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Defining formula

{\displaystyle{\displaystyle b}}

C15.S1.XMD5.m1ddec

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Defining formula

{\displaystyle{\displaystyle c}}

C15.S1.XMD6.m1ddec

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