DLMF:15.4.E33 (Q5017)

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Language	Label	Description	Also known as
English	DLMF:15.4.E33	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle F\left(3a,\tfrac{1}{3}+a;\tfrac{2}{3}+2a;e^{% \ifrac{\mathrm{i}\pi}{3}}\right)=\sqrt{\pi}e^{\ifrac{\mathrm{i}\pi a}{2}}\left% (\frac{16}{27}\right)^{(3a+1)/6}\frac{\Gamma\left(\frac{5}{6}+a\right)}{\Gamma% \left(\frac{2}{3}+a\right)\Gamma\left(\frac{2}{3}\right)},}}

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DLMF:15.4.E33

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Defining formula

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

C5.S2.E1.m2akdec

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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.m2aaedec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2aedec

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base of natural logarithm

Defining formula

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

C4.S2.E11.m2adec

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Defining formula

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

C1.S9.E1.m2adec

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Defining formula

{\displaystyle{\displaystyle a}}

C15.S1.XMD4.m1zdec

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