Formula:5906

Digital Library of Mathematical Functions ID 16.4.E15

${\displaystyle{\displaystyle{{}_{7}F_{6}}\left({a,\frac{1}{2}a+1,b,c,d,e,f\atop\frac{1}{2}a,a-b+1,a-c+1,a-d+1,a-e+1,a-f+1};1\right)=\frac{\Gamma\left(a-d+1\right)\Gamma\left(a-e+1\right)\Gamma\left(a-f+1\right)\Gamma\left(a-d-e-f+1\right)}{\Gamma\left(a+1\right)\Gamma\left(a-d-e+1\right)\Gamma\left(a-d-f+1\right)\Gamma\left(a-e-f+1\right)}{{}_{4}F_{3}}\left({a-b-c+1,d,e,f\atop a-b+1,a-c+1,d+e+f-a};1\right),}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle{{}_{\NVar{p}}F_{\NVar{q}}}\left(\NVar{a_{1},\dots,a_{p}};\NVar{b_{1},\dots,b_{q}};\NVar{z}\right)}}$: 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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