DLMF:14.3.E17 (Q4706)

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Language	Label	Description	Also known as
English	DLMF:14.3.E17	No description defined

Statements

Defining formula

{\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),}}

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DLMF:14.3.E17

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Defining formula

{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

C5.S2.E1.m2ajdec

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Defining formula

{\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}

C14.S21.SS1.p1.m1aedec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2afdec

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$$={{}_{2}{\mathbf{F}}_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Olver’s hypergeometric function

Defining formula

{\displaystyle{\displaystyle\mathbf{F}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z% }\right)}}

C15.S2.E2.m2amdec

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Defining formula

{\displaystyle{\displaystyle x}}

C14.S1.XMD1.m1pdec

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Defining formula

{\displaystyle{\displaystyle\mu}}

C14.S1.XMD7.m1ldec

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Defining formula

{\displaystyle{\displaystyle\nu}}

C14.S1.XMD8.m1odec

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