DLMF:9.12.E12 (Q2940)

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DLMF:9.12.E12
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    Statements

    Defining formula
    Gi ⁡ ( z ) = 1 2 ⁢ e π ⁢ i / 3 ⁢ Hi ⁡ ( z ⁢ e - 2 ⁢ π ⁢ i / 3 ) + 1 2 ⁢ e - π ⁢ i / 3 ⁢ Hi ⁡ ( z ⁢ e 2 ⁢ π ⁢ i / 3 ) , Scorer-Gi 𝑧 1 2 superscript 𝑒 𝜋 𝑖 3 Scorer-Hi 𝑧 superscript 𝑒 2 𝜋 𝑖 3 1 2 superscript 𝑒 𝜋 𝑖 3 Scorer-Hi 𝑧 superscript 𝑒 2 𝜋 𝑖 3 {\displaystyle{\displaystyle\mathrm{Gi}\left(z\right)=\tfrac{1}{2}e^{\pi i/3}% \mathrm{Hi}\left(ze^{-2\pi i/3}\right)+\tfrac{1}{2}e^{-\pi i/3}\mathrm{Hi}% \left(ze^{2\pi i/3}\right),}}
    0 references
    DLMF id
    DLMF:9.12.E12
    0 references
    Symbols used
    Scorer function (inhomogeneous Airy function)
    Defining formula
    Gi ⁡ ( z ) Scorer-Gi 𝑧 {\displaystyle{\displaystyle\mathrm{Gi}\left(\NVar{z}\right)}}
    xml-id
    C9.S12.E4.m2agdec
    0 references
    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.m2ahdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aedec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2acdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2acdec
    0 references
     
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