DLMF:9.12.E27 (Q2955)

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DLMF:9.12.E27
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    Statements

    test
    Hi ⁡ ( z ) ∼ - 1 π ⁢ z ⁢ ∑ k = 0 ∞ ( 3 ⁢ k ) ! k ! ⁢ ( 3 ⁢ z 3 ) k , asymptotic-expansion Scorer-Hi 𝑧 1 𝜋 𝑧 superscript subscript 𝑘 0 3 𝑘 𝑘 superscript 3 superscript 𝑧 3 𝑘 {\displaystyle{\displaystyle\mathrm{Hi}\left(z\right)\sim-\frac{1}{\pi z}\sum_% {k=0}^{\infty}\frac{(3k)!}{k!(3z^{3})^{k}},}}
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    DLMF id
    DLMF:9.12.E27
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    constraint
    | ph ⁡ ( - z ) | ≤ 2 3 ⁢ π - δ phase 𝑧 2 3 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}\left(-z\right)|\leq\tfrac{2}{3}% \pi-\delta}}
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    Symbols used
    Scorer function (inhomogeneous Airy function)
    test
    Hi ⁡ ( z ) Scorer-Hi 𝑧 {\displaystyle{\displaystyle\mathrm{Hi}\left(\NVar{z}\right)}}
    xml-id
    C9.S12.E5.m2apdec
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    Q10931
    test
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11abdec
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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.m2atdec
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    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5afdec
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    Q10817
    test
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1afdec
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    Q11385
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C9.S1.XMD1.m1fdec
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    Q11381
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C9.S1.XMD3.m1vdec
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    Q11386
    test
    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    xml-id
    C9.S1.XMD4.m1bdec
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