DLMF:14.8.E12 (Q4786): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
Property / constraint
 

ν > - 1 2 𝜈 1 2 {\displaystyle{\displaystyle\Re\nu>-\tfrac{1}{2}}}

\Re\nu>-\tfrac{1}{2}
Property / constraint: ν > - 1 2 𝜈 1 2 {\displaystyle{\displaystyle\Re\nu>-\tfrac{1}{2}}} / rank
 
Normal rank

Revision as of 17:51, 30 December 2019

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DLMF:14.8.E12
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    Statements

    P ν μ ( x ) Γ ( ν + 1 2 ) π 1 / 2 Γ ( ν - μ + 1 ) ( 2 x ) ν , asymptotically-equals Legendre-P-first-kind 𝜇 𝜈 𝑥 Euler-Gamma 𝜈 1 2 superscript 𝜋 1 2 Euler-Gamma 𝜈 𝜇 1 superscript 2 𝑥 𝜈 {\displaystyle{\displaystyle P^{\mu}_{\nu}\left(x\right)\sim\frac{\Gamma\left(% \nu+\frac{1}{2}\right)}{\pi^{1/2}\Gamma\left(\nu-\mu+1\right)}(2x)^{\nu},}}
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    DLMF:14.8.E12
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    ν > - 1 2 𝜈 1 2 {\displaystyle{\displaystyle\Re\nu>-\tfrac{1}{2}}}
    0 references
    ν > - 1 2 𝜈 1 2 {\displaystyle{\displaystyle\Re\nu>-\tfrac{1}{2}}}
    0 references