Formula:5760

Digital Library of Mathematical Functions ID 15.8.E6

${\displaystyle{\displaystyle F\left({-m,b\atop c};z\right)=\frac{(b)_{m}}{(c)_{m}}(-z)^{m}F\left({-m,1-c-m\atop 1-b-m};\frac{1}{z}\right)=\frac{(b)_{m}}{(c)_{m}}(1-z)^{m}F\left({-m,c-b\atop 1-b-m};\frac{1}{1-z}\right),}}$

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
• ${\displaystyle{\displaystyle b}}$: real or complex parameter
• ${\displaystyle{\displaystyle c}}$: real or complex parameter
• ${\displaystyle{\displaystyle m}}$: integer
 

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