Formula:5968

Digital Library of Mathematical Functions ID 16.16.E5

${\displaystyle{\displaystyle{F_{3}}\left(\alpha,\gamma-\alpha;\beta,\gamma-\beta;\gamma;x,y\right)=(1-y)^{\alpha+\beta-\gamma}{{}_{2}F_{1}}\left({\alpha,\beta\atop\gamma};x+y-xy\right),}}$

Symbols List

• ${\displaystyle{\displaystyle{F_{3}}\left(\NVar{\alpha},\NVar{\alpha^{\prime}};\NVar{\beta},\NVar{\beta^{\prime}};\NVar{\gamma};\NVar{x},\NVar{y}\right)}}$: third Appell function
• ${\displaystyle{\displaystyle{{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}$: = F ( a , b ; c ; z ) notation for Gauss’ hypergeometric function
 

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