DLMF:9.13.E9 (Q2971)

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DLMF:9.13.E9
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    Statements

    test
    A n ⁡ ( z ) = p / π ⁢ sin ⁡ ( p ⁢ π ) ⁢ z - n / 4 ⁢ e - ζ ⁢ ( 1 + O ⁡ ( ζ - 1 ) ) , ODE-generalized-Airy-A 𝑛 𝑧 𝑝 𝜋 𝑝 𝜋 superscript 𝑧 𝑛 4 superscript 𝑒 𝜁 1 Big-O superscript 𝜁 1 {\displaystyle{\displaystyle A_{n}\left(z\right)=\sqrt{\ifrac{p}{\pi}}\sin% \left(p\pi\right)z^{-n/4}e^{-\zeta}\left(1+O\left(\zeta^{-1}\right)\right),}}
    0 references
    DLMF id
    DLMF:9.13.E9
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    constraint
    | ph ⁡ z | ≤ 3 ⁢ p ⁢ π - δ phase 𝑧 3 𝑝 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq 3p\pi-\delta}}
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    Symbols used
    order not exceeding
    test
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2adec
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    Q11416
    test
    A n ⁡ ( z ) ODE-generalized-Airy-A 𝑛 𝑧 {\displaystyle{\displaystyle A_{\NVar{n}}\left(\NVar{z}\right)}}
    xml-id
    C9.S13.SS1.p2.m3aedec
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    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
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    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
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    Q10817
    test
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1adec
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    sine function
    test
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2abdec
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    Q11381
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C9.S1.XMD3.m1gdec
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    Q11386
    test
    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    xml-id
    C9.S1.XMD4.m1dec
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    parameter (locally)
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C9.S13.XMD1.m1gdec
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    Q11414
    test
    p 𝑝 {\displaystyle{\displaystyle p}}
    xml-id
    C9.S13.XMD3.m1gdec
    0 references
     
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