DLMF:18.15.E12 (Q5704)

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Language	Label	Description	Also known as
English	DLMF:18.15.E12	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle P_{n}\left(\cos\theta\right)=\left(\frac{2}{\sin% \theta}\right)^{\frac{1}{2}}\sum_{m=0}^{M-1}\genfrac{(}{)}{0.0pt}{}{-\tfrac{1}% {2}}{m}\genfrac{(}{)}{0.0pt}{}{m-\frac{1}{2}}{n}\frac{\cos\alpha_{n,m}}{(2\sin% \theta)^{m}}+O\left(\frac{1}{n^{M+\frac{1}{2}}}\right),}}

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DLMF:18.15.E12

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order not exceeding

Defining formula

{\displaystyle{\displaystyle O\left(\NVar{x}\right)}}

C2.S1.E3.m2acdec

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Defining formula

{\displaystyle{\displaystyle P_{\NVar{n}}\left(\NVar{x}\right)}}

C18.S3.T1.t1.r10.m2adec

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Defining formula

{\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}

C1.S2.SS1.m1adec

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cosine function

Defining formula

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

C4.S14.E2.m2addec

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Defining formula

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

C4.S14.E1.m2addec

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Defining formula

{\displaystyle{\displaystyle m}}

C18.S1.XMD5.m1hdec

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Defining formula

{\displaystyle{\displaystyle n}}

C18.S1.XMD6.m1gdec

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Defining formula

{\displaystyle{\displaystyle\alpha_{n,m}}}

C18.S15.XMD10.m1dec

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