DLMF:14.3.E16 (Q4705)

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Language	Label	Description	Also known as
English	DLMF:14.3.E16	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\cos\left(\nu\pi\right)P^{-\mu}_{\nu}\left(x\right% )=\frac{2^{\nu}\pi^{1/2}x^{\nu-\mu}\left(x^{2}-1\right)^{\mu/2}}{\Gamma\left(% \nu+\mu+1\right)}\mathbf{F}\left(\tfrac{1}{2}\mu-\tfrac{1}{2}\nu,\tfrac{1}{2}% \mu-\tfrac{1}{2}\nu+\tfrac{1}{2};\tfrac{1}{2}-\nu;\frac{1}{x^{2}}\right)-\frac% {\pi^{1/2}\left(x^{2}-1\right)^{\mu/2}}{2^{\nu+1}\Gamma\left(\mu-\nu\right)x^{% \nu+\mu+1}}\mathbf{F}\left(\tfrac{1}{2}\nu+\tfrac{1}{2}\mu+1,\tfrac{1}{2}\nu+% \tfrac{1}{2}\mu+\tfrac{1}{2};\nu+\tfrac{3}{2};\frac{1}{x^{2}}\right),}}

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DLMF:14.3.E16

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Defining formula

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

C5.S2.E1.m2aidec

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Defining formula

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

C14.S21.SS1.p1.m1addec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2aedec

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cosine function

Defining formula

{\displaystyle{\displaystyle\cos\NVar{z}}}

C4.S14.E2.m2acdec

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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.m2aldec

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Defining formula

{\displaystyle{\displaystyle x}}

C14.S1.XMD1.m1odec

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Defining formula

{\displaystyle{\displaystyle\mu}}

C14.S1.XMD7.m1kdec

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Sitelinks

Wikipedia(0 entries)

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