DLMF:9.12.E26 (Q2954)

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DLMF:9.12.E26
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    Statements

    Defining formula
    Gi ′ ⁡ ( z ) ∼ - 1 π ⁢ z 2 ⁢ ∑ k = 0 ∞ ( 3 ⁢ k + 1 ) ! k ! ⁢ ( 3 ⁢ z 3 ) k , asymptotic-expansion diffop Scorer-Gi 1 𝑧 1 𝜋 superscript 𝑧 2 superscript subscript 𝑘 0 3 𝑘 1 𝑘 superscript 3 superscript 𝑧 3 𝑘 {\displaystyle{\displaystyle\mathrm{Gi}'\left(z\right)\sim-\frac{1}{\pi z^{2}}% \sum_{k=0}^{\infty}\frac{(3k+1)!}{k!(3z^{3})^{k}},}}
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    DLMF id
    DLMF:9.12.E26
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    constraint
    | ph ⁡ z | ≤ 1 3 ⁢ π - δ phase 𝑧 1 3 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{1}{3}\pi-\delta}}
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    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.m2aodec
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    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11aadec
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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.m2asdec
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    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aedec
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