DLMF:15.9.E22 (Q5112)

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Language	Label	Description	Also known as
English	DLMF:15.9.E22	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\mathbf{F}\left({a,b\atop\tfrac{1}{2}};z\right)=% \frac{2^{a+b-(\ifrac{3}{2})}}{\pi}\Gamma\left(a+\tfrac{1}{2}\right)\Gamma\left% (b+\tfrac{1}{2}\right)\*(z-1)^{(-a-b+(\ifrac{1}{2}))/2}\*\left(e^{\pm\pi% \mathrm{i}(a+b-(\ifrac{1}{2}))}P^{-a-b+(\ifrac{1}{2})}_{a-b-(\ifrac{1}{2})}% \left(-\sqrt{z}\right)+P^{-a-b+(\ifrac{1}{2})}_{a-b-(\ifrac{1}{2})}\left(\sqrt% {z}\right)\right),}}

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DLMF:15.9.E22

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{\displaystyle{\displaystyle 0<|\operatorname{ph}z|<\pi}}

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{\displaystyle{\displaystyle a,b\neq-\frac{1}{2},-\frac{3}{2},-\frac{5}{2},% \ldots}}

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{\displaystyle{\displaystyle 0<|\operatorname{ph}z|<\pi}}

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Defining formula

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

C5.S2.E1.m2acdec

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Defining formula

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

C14.S21.SS1.p1.m1afdec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2agdec

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base of natural logarithm

Defining formula

{\displaystyle{\displaystyle\mathrm{e}}}

C4.S2.E11.m2abdec

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Defining formula

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

C1.S9.E1.m2aedec

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Defining formula

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

C1.S9.E7.m1afdec

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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.m2afdec

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Sitelinks

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