# DLMF:14.3.E17 (Q4706)

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
No description defined
Language Label Description Also known as
English
DLMF:14.3.E17
No description defined

## Statements

${\displaystyle{\displaystyle P^{-\mu}_{\nu}\left(x\right)=\frac{\pi\left(x^{2}% -1\right)^{\mu/2}}{2^{\mu}}\left(\frac{\mathbf{F}\left(\frac{1}{2}\mu-\frac{1}% {2}\nu,\frac{1}{2}\nu+\frac{1}{2}\mu+\frac{1}{2};\frac{1}{2};x^{2}\right)}{% \Gamma\left(\frac{1}{2}\mu-\frac{1}{2}\nu+\frac{1}{2}\right)\Gamma\left(\frac{% 1}{2}\nu+\frac{1}{2}\mu+1\right)}-\frac{x\mathbf{F}\left(\frac{1}{2}\mu-\frac{% 1}{2}\nu+\frac{1}{2},\frac{1}{2}\nu+\frac{1}{2}\mu+1;\frac{3}{2};x^{2}\right)}% {\Gamma\left(\frac{1}{2}\mu-\frac{1}{2}\nu\right)\Gamma\left(\frac{1}{2}\nu+% \frac{1}{2}\mu+\frac{1}{2}\right)}\right),}}$
0 references
DLMF:14.3.E17
0 references
${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$
C5.S2.E1.m2ajdec
0 references
${\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}$
C14.S21.SS1.p1.m1aedec
0 references
${\displaystyle{\displaystyle\pi}}$
C3.S12.E1.m2afdec
0 references
${\displaystyle{\displaystyle\mathbf{F}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z% }\right)}}$
C15.S2.E2.m2amdec
0 references
${\displaystyle{\displaystyle x}}$
C14.S1.XMD1.m1pdec
0 references
${\displaystyle{\displaystyle\mu}}$
C14.S1.XMD7.m1ldec
0 references
${\displaystyle{\displaystyle\nu}}$
C14.S1.XMD8.m1odec
0 references