DLMF:9.12.E25 (Q3651)

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DLMF:9.12.E25
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    Statements

    DLMF defining formula
    Gi ⁡ ( z ) ∼ 1 π ⁢ z ⁢ ∑ k = 0 ∞ ( 3 ⁢ k ) ! k ! ⁢ ( 3 ⁢ z 3 ) k , asymptotic-expansion Scorer-Gi 𝑧 1 𝜋 𝑧 superscript subscript 𝑘 0 3 𝑘 𝑘 superscript 3 superscript 𝑧 3 𝑘 {\displaystyle{\displaystyle\mathrm{Gi}\left(z\right)\sim\frac{1}{\pi z}\sum_{% k=0}^{\infty}\frac{(3k)!}{k!(3z^{3})^{k}},}}
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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)
    DLMF defining formula
    Gi ⁡ ( z ) Scorer-Gi 𝑧 {\displaystyle{\displaystyle\mathrm{Gi}\left(\NVar{z}\right)}}
    xml-id
    C9.S12.E4.m2andec
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    Q10905
    DLMF defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11adec
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    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ardec
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    Q10729
    DLMF defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5addec
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    phase
    DLMF defining formula
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1addec
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    nonnegative integer
    DLMF defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C9.S1.XMD1.m1ddec
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    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C9.S1.XMD3.m1tdec
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    small positive constant
    DLMF defining formula
    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    xml-id
    C9.S1.XMD4.m1dec
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    Identifiers

     
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