DLMF:15.8.E25 (Q5082): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:15.8.E25	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle F\left({a,b\atop\tfrac{1}{2}(a+b+1)};z\right)=% \frac{\Gamma\left(\tfrac{1}{2}(a+b+1)\right)\Gamma\left(\tfrac{1}{2}\right)}{% \Gamma\left(\tfrac{1}{2}a+\tfrac{1}{2}\right)\Gamma\left(\tfrac{1}{2}b+\tfrac{% 1}{2}\right)}F\left({\tfrac{1}{2}a,\tfrac{1}{2}b\atop\tfrac{1}{2}};(1-2z)^{2}% \right)+(1-2z)\frac{\Gamma\left(\tfrac{1}{2}(a+b+1)\right)\Gamma\left(-\tfrac{% 1}{2}\right)}{\Gamma\left(\tfrac{1}{2}a\right)\Gamma\left(\tfrac{1}{2}b\right)% }F\left({\tfrac{1}{2}a+\tfrac{1}{2},\tfrac{1}{2}b+\tfrac{1}{2}\atop\tfrac{3}{2% }};(1-2z)^{2}\right),}}

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DLMF:15.8.E25

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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.m2aidec

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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.m2andec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2aodec

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Defining formula

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

C1.S9.E7.m1aodec

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Sitelinks

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