DLMF:14.25.E1 (Q4958)

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DLMF:14.25.E1
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    test
    P ν - μ ⁡ ( z ) = ( z 2 - 1 ) μ / 2 2 ν ⁢ Γ ⁡ ( μ - ν ) ⁢ Γ ⁡ ( ν + 1 ) ⁢ ∫ 0 ∞ ( sinh ⁡ t ) 2 ⁢ ν + 1 ( z + cosh ⁡ t ) ν + μ + 1 ⁢ d t , Legendre-P-first-kind 𝜇 𝜈 𝑧 superscript superscript 𝑧 2 1 𝜇 2 superscript 2 𝜈 Euler-Gamma 𝜇 𝜈 Euler-Gamma 𝜈 1 superscript subscript 0 superscript 𝑡 2 𝜈 1 superscript 𝑧 𝑡 𝜈 𝜇 1 𝑡 {\displaystyle{\displaystyle P^{-\mu}_{\nu}\left(z\right)=\frac{\left(z^{2}-1% \right)^{\mu/2}}{2^{\nu}\Gamma\left(\mu-\nu\right)\Gamma\left(\nu+1\right)}% \int_{0}^{\infty}\frac{(\sinh t)^{2\nu+1}}{(z+\cosh t)^{\nu+\mu+1}}\mathrm{d}t% ,}}
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    DLMF id
    DLMF:14.25.E1
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