DLMF:14.17.E19 (Q4900): Difference between revisions

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Property / constraint
 

ν - 1 , - 2 , - 3 , 𝜈 1 2 3 {\displaystyle{\displaystyle\nu\neq-1,-2,-3,\dots}}

\nu\neq-1,-2,-3,\dots
Property / constraint: ν - 1 , - 2 , - 3 , 𝜈 1 2 3 {\displaystyle{\displaystyle\nu\neq-1,-2,-3,\dots}} / rank
 
Normal rank

Revision as of 16:53, 30 December 2019

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DLMF:14.17.E19
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    Statements

    1 Q ν ( x ) Q λ ( x ) d x = ψ ( λ + 1 ) - ψ ( ν + 1 ) ( λ - ν ) ( λ + ν + 1 ) , superscript subscript 1 shorthand-Legendre-Q-second-kind 𝜈 𝑥 shorthand-Legendre-Q-second-kind 𝜆 𝑥 𝑥 digamma 𝜆 1 digamma 𝜈 1 𝜆 𝜈 𝜆 𝜈 1 {\displaystyle{\displaystyle\int_{1}^{\infty}Q_{\nu}\left(x\right)Q_{\lambda}% \left(x\right)\mathrm{d}x=\frac{\psi\left(\lambda+1\right)-\psi\left(\nu+1% \right)}{(\lambda-\nu)(\lambda+\nu+1)},}}
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    ( λ + ν ) > - 1 𝜆 𝜈 1 {\displaystyle{\displaystyle\Re(\lambda+\nu)>-1}}
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    λ 𝜆 {\displaystyle{\displaystyle\lambda}}
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    ν - 1 , - 2 , - 3 , 𝜈 1 2 3 {\displaystyle{\displaystyle\nu\neq-1,-2,-3,\dots}}
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