Formula:5773

Digital Library of Mathematical Functions ID 15.8.E19

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

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
 

Resources that cite this formula

No records found.