DLMF:14.12.E8 (Q4829)

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Language	Label	Description	Also known as
English	DLMF:14.12.E8	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle P^{m}_{n}\left(x\right)=\frac{2^{m}m!(n+m)!\left(% x^{2}-1\right)^{m/2}}{(2m)!(n-m)!\pi}\int_{0}^{\pi}\left(x+\left(x^{2}-1\right% )^{1/2}\cos\phi\right)^{n-m}(\sin\phi)^{2m}\mathrm{d}\phi,}}

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DLMF:14.12.E8

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{\displaystyle{\displaystyle n\geq m}}

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Defining formula

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

C14.S21.SS1.p1.m1acdec

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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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Defining formula

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

C1.S4.SS4.m1agdec

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Defining formula

{\displaystyle{\displaystyle!}}

introduction.Sx4.p1.t1.r15.m5adec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3agdec

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Sitelinks

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