Formula:5937

Digital Library of Mathematical Functions ID 16.11.E6

${\displaystyle{\displaystyle\left({\textstyle\ifrac{\prod\limits_{\ell=1}^{q+1}\Gamma\left(a_{\ell}\right)}{\prod\limits_{\ell=1}^{q}\Gamma\left(b_{\ell}\right)}}\right){{}_{q+1}F_{q}}\left({a_{1},\dots,a_{q+1}\atop b_{1},\dots,b_{q}};z\right)=H_{q+1,q}(-z),}}$

Constraint(s)

${\displaystyle{\displaystyle|\operatorname{ph}\left(-z\right)|\leq\pi}}$

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
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\operatorname{ph}}}$: phase
• ${\displaystyle{\displaystyle q}}$: nonnegative integer
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle a,a_{1},\ldots,a_{p}}}$: real or complex parameters
• ${\displaystyle{\displaystyle b,b_{1},\ldots,b_{q}}}$: real or complex parameters
• ${\displaystyle{\displaystyle H_{p,q}(z)}}$: formal infinite series (locally)
 

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