DLMF:15.16.E5 (Q5182)

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Language	Label	Description	Also known as
English	DLMF:15.16.E5	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle F\left({\frac{1}{2}+\lambda,-\frac{1}{2}-\nu\atop 1% +\lambda+\mu};z\right)F\left({\frac{1}{2}-\lambda,\frac{1}{2}+\nu\atop 1+\nu+% \mu};1-z\right)+F\left({\frac{1}{2}+\lambda,\frac{1}{2}-\nu\atop 1+\lambda+\mu% };z\right)F\left({-\frac{1}{2}-\lambda,\frac{1}{2}+\nu\atop 1+\nu+\mu};1-z% \right)-F\left({\frac{1}{2}+\lambda,\frac{1}{2}-\nu\atop 1+\lambda+\mu};z% \right)F\left({\frac{1}{2}-\lambda,\frac{1}{2}+\nu\atop 1+\nu+\mu};1-z\right)=% \frac{\Gamma\left(1+\lambda+\mu\right)\Gamma\left(1+\nu+\mu\right)}{\Gamma% \left(\lambda+\mu+\nu+\frac{3}{2}\right)\Gamma\left(\frac{1}{2}+\nu\right)},}}

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DLMF:15.16.E5

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

C5.S2.E1.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.m2addec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2adec

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Defining formula

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

C1.S9.E7.m1adec

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Defining formula

{\displaystyle{\displaystyle z}}

C15.S1.XMD3.m1ddec

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