DLMF:9.13.E12 (Q2974)

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DLMF:9.13.E12
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    Statements

    Defining formula
    B n ⁡ ( - z ) = { - ( 2 / π ) ⁢ sin ⁡ ( 1 2 ⁢ p ⁢ π ) ⁢ z - n / 4 ⁢ ( sin ⁡ ( ζ - 1 4 ⁢ π ) + e | ℑ ⁡ ζ | ⁢ O ⁡ ( ζ - 1 ) ) , | ph ⁡ z | ≤ 2 ⁢ p ⁢ π - δ , n ⁢  odd , ( 1 / π ) ⁢ sin ⁡ ( p ⁢ π ) ⁢ z - n / 4 ⁢ e - ζ ⁢ ( 1 + O ⁡ ( ζ - 1 ) ) , | ph ⁡ z | ≤ 3 ⁢ p ⁢ π - δ , n ⁢  even . ODE-generalized-Airy-B 𝑛 𝑧 cases 2 𝜋 1 2 𝑝 𝜋 superscript 𝑧 𝑛 4 𝜁 1 4 𝜋 superscript 𝑒 𝜁 Big-O superscript 𝜁 1 phase 𝑧 2 𝑝 𝜋 𝛿 𝑛  odd 1 𝜋 𝑝 𝜋 superscript 𝑧 𝑛 4 superscript 𝑒 𝜁 1 Big-O superscript 𝜁 1 phase 𝑧 3 𝑝 𝜋 𝛿 𝑛  even {\displaystyle{\displaystyle B_{n}\left(-z\right)=\begin{cases}-(\ifrac{2}{% \sqrt{\pi}})\sin\left(\tfrac{1}{2}p\pi\right)z^{-n/4}\left(\sin\left(\zeta-% \tfrac{1}{4}\pi\right)+e^{\left|\Im\zeta\right|}O\left(\zeta^{-1}\right)\right% ),&\left|\operatorname{ph}z\right|\leq 2p\pi-\delta,n\text{ odd},\\ (\ifrac{1}{\sqrt{\pi}})\sin\left(p\pi\right)z^{-n/4}e^{-\zeta}\left(1+O\left(% \zeta^{-1}\right)\right),&\left|\operatorname{ph}z\right|\leq 3p\pi-\delta,n% \text{ even}.\end{cases}}}
    0 references
    DLMF id
    DLMF:9.13.E12
    0 references
    Symbols used
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2acdec
    0 references
     
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