DLMF:14.12.E5 (Q4826): Difference between revisions

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Property / constraint
 

μ > 0 𝜇 0 {\displaystyle{\displaystyle\Re\mu>0}}

\realpart@@{\mu}>0
Property / constraint: μ > 0 𝜇 0 {\displaystyle{\displaystyle\Re\mu>0}} / rank
 
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Revision as of 16:52, 30 December 2019

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DLMF:14.12.E5
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    Statements

    P ν - μ ( x ) = ( x 2 - 1 ) - μ / 2 Γ ( μ ) 1 x P ν ( t ) ( x - t ) μ - 1 d t , Legendre-P-first-kind 𝜇 𝜈 𝑥 superscript superscript 𝑥 2 1 𝜇 2 Euler-Gamma 𝜇 superscript subscript 1 𝑥 Legendre-spherical-polynomial 𝜈 𝑡 superscript 𝑥 𝑡 𝜇 1 𝑡 {\displaystyle{\displaystyle P^{-\mu}_{\nu}\left(x\right)=\frac{\left(x^{2}-1% \right)^{-\mu/2}}{\Gamma\left(\mu\right)}\int_{1}^{x}P_{\nu}\left(t\right)(x-t% )^{\mu-1}\mathrm{d}t,}}
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    μ > 0 𝜇 0 {\displaystyle{\displaystyle\Re\mu>0}}
    0 references