DLMF:9.12.E9 (Q2937)

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DLMF:9.12.E9
No description defined

    Statements

    Defining formula
    Hi ⁡ ( z ) , Ai ⁡ ( z ⁢ e - 2 ⁢ π ⁢ i / 3 ) , Ai ⁡ ( z ⁢ e 2 ⁢ π ⁢ i / 3 ) , Scorer-Hi 𝑧 Airy-Ai 𝑧 superscript 𝑒 2 𝜋 𝑖 3 Airy-Ai 𝑧 superscript 𝑒 2 𝜋 𝑖 3 {\displaystyle{\displaystyle\mathrm{Hi}\left(z\right),\mathrm{Ai}\left(ze^{-2% \pi i/3}\right),\mathrm{Ai}\left(ze^{2\pi i/3}\right),}}
    0 references
    DLMF id
    DLMF:9.12.E9
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    constraint
    | ph ⁡ ( - z ) | ≤ 2 3 ⁢ π phase 𝑧 2 3 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}\left(-z\right)|\leq\tfrac{2}{3}% \pi}}
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    Symbols used
    Q10919
    Defining formula
    Ai ⁡ ( z ) Airy-Ai 𝑧 {\displaystyle{\displaystyle\mathrm{Ai}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m1acdec
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    Scorer function (inhomogeneous Airy function)
    Defining formula
    Hi ⁡ ( z ) Scorer-Hi 𝑧 {\displaystyle{\displaystyle\mathrm{Hi}\left(\NVar{z}\right)}}
    xml-id
    C9.S12.E5.m2aedec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
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    Q10817
    Defining formula
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1aadec
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    Q11381
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C9.S1.XMD3.m1fdec
    0 references
     
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