DLMF:14.12.E1 (Q4822)

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Language	Label	Description	Also known as
English	DLMF:14.12.E1	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\mathsf{P}^{\mu}_{\nu}\left(\cos\theta\right)=% \frac{2^{1/2}(\sin\theta)^{\mu}}{\pi^{1/2}\Gamma\left(\frac{1}{2}-\mu\right)}% \int_{0}^{\theta}\frac{\cos\left(\left(\nu+\frac{1}{2}\right)t\right)}{(\cos t% -\cos\theta)^{\mu+(1/2)}}\mathrm{d}t,}}

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DLMF:14.12.E1

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{\displaystyle{\displaystyle\Re\mu<\tfrac{1}{2}}}

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{\displaystyle{\displaystyle 0<\theta<\pi}}

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{\displaystyle{\displaystyle\Re\mu<\tfrac{1}{2}}}

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Defining formula

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

C5.S2.E1.m2adec

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Ferrers function of the first kind

Defining formula

{\displaystyle{\displaystyle\mathsf{P}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}% \right)}}

C14.S3.E1.m2adec

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2adec

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cosine function

Defining formula

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

C4.S14.E2.m2adec

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Defining formula

{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

C1.S4.SS4.m1adec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3adec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1adec

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Defining formula

{\displaystyle{\displaystyle\sin\NVar{z}}}

C4.S14.E1.m2adec

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Defining formula

{\displaystyle{\displaystyle\mu}}

C14.S1.XMD7.m1dec

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Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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