DLMF:9.7.E7 (Q3512)

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DLMF:9.7.E7
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    Statements

    DLMF defining formula
    Bi ⁡ ( z ) ∼ e ζ π ⁢ z 1 / 4 ⁢ ∑ k = 0 ∞ u k ζ k , asymptotic-expansion Airy-Bi 𝑧 superscript 𝑒 𝜁 𝜋 superscript 𝑧 1 4 superscript subscript 𝑘 0 subscript 𝑢 𝑘 superscript 𝜁 𝑘 {\displaystyle{\displaystyle\mathrm{Bi}\left(z\right)\sim\frac{e^{\zeta}}{% \sqrt{\pi}z^{1/4}}\sum_{k=0}^{\infty}\frac{u_{k}}{\zeta^{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
    Q11055
    DLMF defining formula
    Bi ⁡ ( z ) Airy-Bi 𝑧 {\displaystyle{\displaystyle\mathrm{Bi}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m2adec
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    Q10905
    DLMF defining formula
    ∼ 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
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
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    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
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    phase
    DLMF defining formula
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1abdec
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    nonnegative integer
    DLMF defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C9.S1.XMD1.m1cdec
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    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C9.S1.XMD3.m1cdec
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    small positive constant
    DLMF defining formula
    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    xml-id
    C9.S1.XMD4.m1bdec
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    change of variable (locally)
    DLMF defining formula
    ζ 𝜁 {\displaystyle{\displaystyle\zeta}}
    xml-id
    C9.S7.XMD1.m1cdec
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    expansion coefficient
    DLMF defining formula
    u s subscript 𝑢 𝑠 {\displaystyle{\displaystyle u_{s}}}
    xml-id
    C9.S7.XMD2.m1bdec
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    Identifiers

     
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