Formula:5761

Digital Library of Mathematical Functions ID 15.8.E7

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

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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