DLMF:9.9.E14 (Q3573)

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DLMF:9.9.E14
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    Statements

    DLMF defining formula
    β k = e π ⁢ i / 3 ⁢ T ⁢ ( 3 8 ⁢ π ⁢ ( 4 ⁢ k - 1 ) + 3 4 ⁢ i ⁢ ln ⁡ 2 ) , complex-zero-Airy-Bi 𝑘 superscript 𝑒 𝜋 𝑖 3 𝑇 3 8 𝜋 4 𝑘 1 3 4 𝑖 2 {\displaystyle{\displaystyle\beta_{k}=e^{\pi i/3}T\left(\tfrac{3}{8}\pi(4k-1)+% \tfrac{3}{4}i\ln 2\right),}}
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aldec
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    Q11369
    DLMF defining formula
    β k complex-zero-Airy-Bi 𝑘 {\displaystyle{\displaystyle\beta_{\NVar{k}}}}
    xml-id
    C9.S9.SS1.p2.m7adec
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    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
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    imaginary unit
    DLMF defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
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    principal branch of logarithm function
    DLMF defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2adec
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    nonnegative integer
    DLMF defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C9.S1.XMD1.m1mdec
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    expansion (locally)
    DLMF defining formula
    T 𝑇 {\displaystyle{\displaystyle T}}
    xml-id
    C9.S9.XMD2.m1bdec
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    Identifiers

     
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