Formula:5803

Digital Library of Mathematical Functions ID 15.9.E16

${\displaystyle{\displaystyle\mathbf{F}\left({a,b\atop 2b};z\right)=\frac{\sqrt{\pi}}{\Gamma\left(b\right)}z^{-b+(\ifrac{1}{2})}(1-z)^{(b-a-(\ifrac{1}{2}))/2}\*P^{-b+(\ifrac{1}{2})}_{a-b-(\ifrac{1}{2})}\left(\frac{2-z}{2\sqrt{1-z}}\right),}}$

Constraint(s)

${\displaystyle{\displaystyle|\operatorname{ph}\left(1-z\right)|<\pi}}$
${\displaystyle{\displaystyle|\operatorname{ph}\left(1-z\right)|<\pi}}$
${\displaystyle{\displaystyle|1-z|<1}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}$: associated Legendre function of the first kind
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\operatorname{ph}}}$: phase
• ${\displaystyle{\displaystyle\mathbf{F}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}$: Olver’s hypergeometric function
• ${\displaystyle{\displaystyle z}}$: complex variable
• ${\displaystyle{\displaystyle a}}$: real or complex parameter
• ${\displaystyle{\displaystyle b}}$: real or complex parameter
 

Resources that cite this formula

No records found.