DLMF:14.20.E15 (Q4936)

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DLMF:14.20.E15
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    Statements

    Defining formula
    𝖯 - 1 2 + i ⁢ τ - μ ⁡ ( cos ⁡ θ ) = 1 τ μ ⁢ ( θ sin ⁡ θ ) 1 / 2 ⁢ I μ ⁡ ( τ ⁢ θ ) ⁢ ( 1 + O ⁡ ( 1 / τ ) ) , Ferrers-Legendre-P-first-kind 𝜇 1 2 𝑖 𝜏 𝜃 1 superscript 𝜏 𝜇 superscript 𝜃 𝜃 1 2 modified-Bessel-first-kind 𝜇 𝜏 𝜃 1 Big-O 1 𝜏 {\displaystyle{\displaystyle\mathsf{P}^{-\mu}_{-\frac{1}{2}+i\tau}\left(\cos% \theta\right)=\frac{1}{\tau^{\mu}}\left(\frac{\theta}{\sin\theta}\right)^{1/2}% I_{\mu}\left(\tau\theta\right)\*\left(1+O\left(\ifrac{1}{\tau}\right)\right),}}
    0 references
    DLMF id
    DLMF:14.20.E15
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    Symbols used
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2adec
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