DLMF:14.15.E11 (Q4857)

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Language	Label	Description	Also known as
English	DLMF:14.15.E11	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\mathsf{P}^{-\mu}_{\nu}\left(\cos\theta\right)=% \frac{1}{\nu^{\mu}}\left(\frac{\theta}{\sin\theta}\right)^{1/2}\left(J_{\mu}% \left(\left(\nu+\tfrac{1}{2}\right)\theta\right)+O\left(\frac{1}{\nu}\right)% \mathrm{env}\mskip-2.0mu J_{\mu}\left(\left(\nu+\tfrac{1}{2}\right)\theta% \right)\right),}}

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DLMF:14.15.E11

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Bessel function of the first kind

Defining formula

{\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}

C10.S2.E2.m2adec

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order not exceeding

Defining formula

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

C2.S1.E3.m2afdec

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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.m2abdec

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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{env}\mskip-2.0mu J_{\NVar{\nu}}\left(\NVar% {x}\right)}}

C2.S8.SS4.p5.m2adec

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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.m1gdec

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Defining formula

{\displaystyle{\displaystyle\nu}}

C14.S1.XMD8.m1gdec

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Defining formula

{\displaystyle{\displaystyle\theta}}

C14.S15.XMD7.m1dec

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Sitelinks

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