DLMF:16.4.E11

MaRDI QIDQ5902

• Label: DLMF:16.4.E11

Digital Library of Mathematical Functions ID 16.4.E11

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

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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