DLMF:15.9.E19 (Q5109)

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Language	Label	Description	Also known as
English	DLMF:15.9.E19	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\mathbf{F}\left({a,b\atop a-b+1};z\right)=z^{% \ifrac{(b-a)}{2}}(1-z)^{-b}\*P^{b-a}_{-b}\left(\frac{1+z}{1-z}\right),}}

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DLMF:15.9.E19

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{\displaystyle{\displaystyle|\operatorname{ph}z|<\pi}}

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{\displaystyle{\displaystyle|\operatorname{ph}\left(1-z\right)|<\pi}}

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Defining formula

{\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}

C14.S21.SS1.p1.m1acdec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2addec

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Defining formula

{\displaystyle{\displaystyle\operatorname{ph}}}

C1.S9.E7.m1acdec

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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.m2acdec

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Defining formula

{\displaystyle{\displaystyle z}}

C15.S1.XMD3.m1ddec

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