DLMF:15.8.E26 (Q5083): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:15.8.E26	No description defined

Statements

Defining formula

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

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DLMF:15.8.E26

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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.m2ajdec

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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.m2aodec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2apdec

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Defining formula

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

C1.S9.E7.m1apdec

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Defining formula

{\displaystyle{\displaystyle z}}

C15.S1.XMD3.m1ydec

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Defining formula

{\displaystyle{\displaystyle a}}

C15.S1.XMD4.m1xdec

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Defining formula

{\displaystyle{\displaystyle c}}

C15.S1.XMD6.m1mdec

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