DLMF:15.8.E24 (Q5081): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:15.8.E24	No description defined

Statements

Defining formula

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

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DLMF:15.8.E24

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

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Defining formula

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

C5.S2.E1.m2ahdec

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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.m2amdec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2andec

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Defining formula

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

C1.S9.E7.m1andec

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Defining formula

{\displaystyle{\displaystyle z}}

C15.S1.XMD3.m1wdec

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Sitelinks

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