DLMF:18.15.E7 (Q5697)

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DLMF:18.15.E7
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    Defining formula
    ε M ⁢ ( ρ , θ ) = { θ ⁢ O ⁡ ( ρ - 2 ⁢ M - ( 3 / 2 ) ) , c ⁢ ρ - 1 ≤ θ ≤ π - δ , θ α + ( 5 / 2 ) ⁢ O ⁡ ( ρ - 2 ⁢ M + α ) , 0 ≤ θ ≤ c ⁢ ρ - 1 , subscript 𝜀 𝑀 𝜌 𝜃 cases 𝜃 Big-O superscript 𝜌 2 𝑀 3 2 𝑐 superscript 𝜌 1 𝜃 𝜋 𝛿 superscript 𝜃 𝛼 5 2 Big-O superscript 𝜌 2 𝑀 𝛼 0 𝜃 𝑐 superscript 𝜌 1 {\displaystyle{\displaystyle\varepsilon_{M}(\rho,\theta)=\begin{cases}\theta O% \left(\rho^{-2M-(3/2)}\right),&c\rho^{-1}\leq\theta\leq\pi-\delta,\\ \theta^{\alpha+(5/2)}O\left(\rho^{-2M+\alpha}\right),&0\leq\theta\leq c\rho^{-% 1},\end{cases}}}
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    DLMF id
    DLMF:18.15.E7
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