DLMF:14.25.E2 (Q4959)

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DLMF:14.25.E2
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    𝑸 ν μ ( z ) = π 1 / 2 ( z 2 - 1 ) μ / 2 2 μ Γ ( μ + 1 2 ) Γ ( ν - μ + 1 ) 0 ( sinh t ) 2 μ ( z + ( z 2 - 1 ) 1 / 2 cosh t ) ν + μ + 1 d t , associated-Legendre-black-Q 𝜇 𝜈 𝑧 superscript 𝜋 1 2 superscript superscript 𝑧 2 1 𝜇 2 superscript 2 𝜇 Euler-Gamma 𝜇 1 2 Euler-Gamma 𝜈 𝜇 1 superscript subscript 0 superscript 𝑡 2 𝜇 superscript 𝑧 superscript superscript 𝑧 2 1 1 2 𝑡 𝜈 𝜇 1 𝑡 {\displaystyle{\displaystyle\boldsymbol{Q}^{\mu}_{\nu}\left(z\right)=\frac{\pi% ^{1/2}\left(z^{2}-1\right)^{\mu/2}}{2^{\mu}\Gamma\left(\mu+\frac{1}{2}\right)% \Gamma\left(\nu-\mu+1\right)}\*\int_{0}^{\infty}\frac{(\sinh t)^{2\mu}}{\left(% z+(z^{2}-1)^{1/2}\cosh t\right)^{\nu+\mu+1}}\mathrm{d}t,}}
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    DLMF:14.25.E2
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