Formula:5774

Digital Library of Mathematical Functions ID 15.8.E20

${\displaystyle{\displaystyle F\left({a,1-a\atop c};z\right)=(1-z)^{c-1}F\left({\frac{1}{2}(c-a),\frac{1}{2}(a+c-1)\atop c};4z(1-z)\right),}}$

Constraint(s)

${\displaystyle{\displaystyle\Re z<\frac{1}{2}}}$

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
• ${\displaystyle{\displaystyle\Re}}$: real part
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle a}}$: real or complex parameter
• ${\displaystyle{\displaystyle c}}$: real or complex parameter
 

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