DLMF:14.17.E14 (Q4895): Difference between revisions

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Language	Label	Description	Also known as
English	DLMF:14.17.E14	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{-1}^{1}\mathsf{P}_{\nu}\left(x\right)\mathsf% {Q}_{\lambda}\left(x\right)\mathrm{d}x=\frac{2\sin\left(\nu\pi\right)\cos\left% (\lambda\pi\right)\left(\psi\left(\nu+1\right)-\psi\left(\lambda+1\right)% \right)+\pi\cos\left((\lambda-\nu)\pi\right)-\pi}{\pi(\lambda-\nu)(\lambda+\nu% +1)},}}

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DLMF:14.17.E14

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{\displaystyle{\displaystyle\Re\lambda>0}}

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{\displaystyle{\displaystyle\Re\nu>0}}

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{\displaystyle{\displaystyle\Re\lambda>0}}

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{\displaystyle{\displaystyle\Re\nu>0}}

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{\displaystyle{\displaystyle\lambda\neq\nu}}

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the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2addec

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cosine function

Defining formula

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

C4.S14.E2.m2abdec

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Defining formula

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

C1.S4.SS4.m1amdec

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psi (or digamma) function

Defining formula

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

C5.S2.E2.m2addec

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Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3amdec

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Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1aadec

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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.m2abdec

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Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

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