DLMF:14.11.E4 (Q4820)

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Language	Label	Description	Also known as
English	DLMF:14.11.E4	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\left.\frac{\partial}{\partial\mu}\mathsf{P}^{\mu}% _{\nu}\left(x\right)\right|_{\mu=0}=\left(\psi\left(-\nu\right)-\pi\cot\left(% \nu\pi\right)\right)\mathsf{P}_{\nu}\left(x\right)+\mathsf{Q}_{\nu}\left(x% \right),}}

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DLMF:14.11.E4

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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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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2acdec

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cotangent function

Defining formula

{\displaystyle{\displaystyle\cot\NVar{z}}}

C4.S14.E7.m2abdec

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psi (or digamma) function

Defining formula

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

C5.S2.E2.m2aadec

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partial derivative of $$f$$ with respect to $$x$$

Defining formula

{\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}

C1.S5.E3.m4abdec

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partial differential of $$x$$

Defining formula

{\displaystyle{\displaystyle\partial\NVar{x}}}

C1.S5.E3.m2abdec

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Defining formula

{\displaystyle{\displaystyle\mathsf{P}_{\NVar{\nu}}\left(\NVar{x}\right)=% \mathsf{P}^{0}_{\nu}\left(x\right)}}

C14.S2.SS2.p2.m2adec

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Defining formula

{\displaystyle{\displaystyle\mathsf{Q}_{\NVar{\nu}}\left(\NVar{x}\right)=% \mathsf{Q}^{0}_{\nu}\left(x\right)}}

C14.S2.SS2.p2.m4adec

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Defining formula

{\displaystyle{\displaystyle x}}

C14.S1.XMD1.m1cdec

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Defining formula

{\displaystyle{\displaystyle\mu}}

C14.S1.XMD7.m1cdec

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Defining formula

{\displaystyle{\displaystyle\nu}}

C14.S1.XMD8.m1cdec

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Sitelinks

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