DLMF:14.17.E11 (Q4892): Difference between revisions

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Property / constraint
 

ν - 1 2 𝜈 1 2 {\displaystyle{\displaystyle\nu\neq-\frac{1}{2}}}

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

Revision as of 16:53, 30 December 2019

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DLMF:14.17.E11
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    Statements

    - 1 1 ( 𝖯 ν ( x ) ) 2 d x = π 2 - 2 sin 2 ( ν π ) ψ ( ν + 1 ) π 2 ( ν + 1 2 ) , superscript subscript 1 1 superscript shorthand-Ferrers-Legendre-P-first-kind 𝜈 𝑥 2 𝑥 superscript 𝜋 2 2 2 𝜈 𝜋 diffop digamma 1 𝜈 1 superscript 𝜋 2 𝜈 1 2 {\displaystyle{\displaystyle\int_{-1}^{1}\left(\mathsf{P}_{\nu}\left(x\right)% \right)^{2}\mathrm{d}x=\frac{\pi^{2}-2{\sin^{2}}\left(\nu\pi\right)\psi'\left(% \nu+1\right)}{\pi^{2}\left(\nu+\frac{1}{2}\right)},}}
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    ν - 1 2 𝜈 1 2 {\displaystyle{\displaystyle\nu\neq-\frac{1}{2}}}
    0 references