Formula:5783

Digital Library of Mathematical Functions ID 15.8.E29

${\displaystyle{\displaystyle F\left({a,\tfrac{1}{3}a+\tfrac{1}{3}\atop\tfrac{2}{3}a+\tfrac{2}{3}};z\right)=\left(1+\sqrt{z}\right)^{-2a}\*F\left({a,\tfrac{2}{3}a+\tfrac{1}{6}\atop\tfrac{4}{3}a+\tfrac{1}{3}};\frac{4\sqrt{z}}{(1+\sqrt{z})^{2}}\right).}}$

Symbols List

• ${\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}$: $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle a}}$: real or complex parameter
 

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