DLMF:13.7.E13 (Q4425)

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DLMF:13.7.E13
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    Statements

    Defining formula
    R m , n ⁢ ( a , b , z ) = { O ⁡ ( e - | z | ⁢ z - m ) , | ph ⁡ z | ≤ π , O ⁡ ( e z ⁢ z - m ) , π ≤ | ph ⁡ z | ≤ 5 2 ⁢ π - δ . subscript 𝑅 𝑚 𝑛 𝑎 𝑏 𝑧 cases Big-O superscript 𝑒 𝑧 superscript 𝑧 𝑚 phase 𝑧 𝜋 Big-O superscript 𝑒 𝑧 superscript 𝑧 𝑚 𝜋 phase 𝑧 5 2 𝜋 𝛿 {\displaystyle{\displaystyle R_{m,n}(a,b,z)=\begin{cases}O\left(e^{-|z|}z^{-m}% \right),&|\operatorname{ph}z|\leq\pi,\\ O\left(e^{z}z^{-m}\right),&\pi\leq|\operatorname{ph}z|\leq\tfrac{5}{2}\pi-% \delta.\\ \end{cases}}}
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    DLMF id
    DLMF:13.7.E13
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