DLMF:14.15.E13 (Q4859)

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DLMF:14.15.E13
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    Defining formula
    P ν - μ ⁡ ( cosh ⁡ ξ ) = 1 ν μ ⁢ ( ξ sinh ⁡ ξ ) 1 / 2 ⁢ I μ ⁡ ( ( ν + 1 2 ) ⁢ ξ ) ⁢ ( 1 + O ⁡ ( 1 ν ) ) , Legendre-P-first-kind 𝜇 𝜈 𝜉 1 superscript 𝜈 𝜇 superscript 𝜉 𝜉 1 2 modified-Bessel-first-kind 𝜇 𝜈 1 2 𝜉 1 Big-O 1 𝜈 {\displaystyle{\displaystyle P^{-\mu}_{\nu}\left(\cosh\xi\right)=\frac{1}{\nu^% {\mu}}\left(\frac{\xi}{\sinh\xi}\right)^{1/2}I_{\mu}\left(\left(\nu+\tfrac{1}{% 2}\right)\xi\right)\*\left(1+O\left(\frac{1}{\nu}\right)\right),}}
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    DLMF id
    DLMF:14.15.E13
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