DLMF:14.17.E18 (Q4899): Difference between revisions

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Property / constraint
 

λ > ν > 0 𝜆 𝜈 0 {\displaystyle{\displaystyle\Re\lambda>\Re\nu>0}}

\realpart@@{\lambda}>\realpart@@{\nu}>0
Property / constraint: λ > ν > 0 𝜆 𝜈 0 {\displaystyle{\displaystyle\Re\lambda>\Re\nu>0}} / rank
 
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Revision as of 16:53, 30 December 2019

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DLMF:14.17.E18
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    Statements

    1 P ν ( x ) Q λ ( x ) d x = 1 ( λ - ν ) ( ν + λ + 1 ) , superscript subscript 1 shorthand-Legendre-P-first-kind 𝜈 𝑥 shorthand-Legendre-Q-second-kind 𝜆 𝑥 𝑥 1 𝜆 𝜈 𝜈 𝜆 1 {\displaystyle{\displaystyle\int_{1}^{\infty}P_{\nu}\left(x\right)Q_{\lambda}% \left(x\right)\mathrm{d}x=\frac{1}{(\lambda-\nu)(\nu+\lambda+1)},}}
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    λ > ν > 0 𝜆 𝜈 0 {\displaystyle{\displaystyle\Re\lambda>\Re\nu>0}}
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