Formula:5903

Digital Library of Mathematical Functions ID 16.4.E12

${\displaystyle{\displaystyle(a-d)(b-d)(c-d)\left({{}_{3}F_{2}}\left({a,b,c\atop d+1,e};1\right)-{{}_{3}F_{2}}\left({a,b,c\atop d,e};1\right)\right)+abc{{}_{3}F_{2}}\left({a,b,c\atop d,e};1\right)=d(d-1)(a+b+c-d-e+1)\left({{}_{3}F_{2}}\left({a,b,c\atop d,e};1\right)-{{}_{3}F_{2}}\left({a,b,c\atop d-1,e};1\right)\right),}}$

Symbols List

• ${\displaystyle{\displaystyle{{}_{\NVar{p}}F_{\NVar{q}}}\left(\NVar{a_{1},\dots,a_{p}};\NVar{b_{1},\dots,b_{q}};\NVar{z}\right)}}$: alternatively F q p ( a ; b ; z ) or F q p ( a b ; z ) generalized hypergeometric function
• ${\displaystyle{\displaystyle a}}$: real or complex parameters
• ${\displaystyle{\displaystyle b}}$: real or complex parameters
• ${\displaystyle{\displaystyle c}}$: real or complex parameters
• ${\displaystyle{\displaystyle d}}$: real or complex parameters
• ${\displaystyle{\displaystyle e}}$: real or complex parameters
 

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