DLMF:9.9.E16 (Q2877)

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DLMF:9.9.E16
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    Statements

    Defining formula
    β k ′ = e π ⁢ i / 3 ⁢ U ⁢ ( 3 8 ⁢ π ⁢ ( 4 ⁢ k - 3 ) + 3 4 ⁢ i ⁢ ln ⁡ 2 ) , complex-zero-derivative-Airy-Bi 𝑘 superscript 𝑒 𝜋 𝑖 3 𝑈 3 8 𝜋 4 𝑘 3 3 4 𝑖 2 {\displaystyle{\displaystyle\beta^{\prime}_{k}=e^{\pi i/3}U\left(\tfrac{3}{8}% \pi(4k-3)+\tfrac{3}{4}i\ln 2\right),}}
    0 references
    DLMF id
    DLMF:9.9.E16
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2andec
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    Q11399
    Defining formula
    β k ′ complex-zero-derivative-Airy-Bi 𝑘 {\displaystyle{\displaystyle\beta^{\prime}_{\NVar{k}}}}
    xml-id
    C9.S9.SS1.p2.m10adec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2abdec
    0 references
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2abdec
    0 references
    Q11385
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C9.S1.XMD1.m1odec
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    expansion (locally)
    Defining formula
    U 𝑈 {\displaystyle{\displaystyle U}}
    xml-id
    C9.S9.XMD3.m1bdec
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