DLMF:9.9.E17 (Q2878): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: expansion (locally) / rank
 
Normal rank
Property / Symbols used: expansion (locally) / qualifier
 
Defining formula:

W 𝑊 {\displaystyle{\displaystyle W}}

W
Property / Symbols used: expansion (locally) / qualifier
 
xml-id: C9.S9.XMD5.m1bdec

Latest revision as of 14:43, 2 January 2020

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DLMF:9.9.E17
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    Statements

    Defining formula
    Bi ⁡ ( β k ′ ) = ( - 1 ) k - 1 ⁢ 2 ⁢ e π ⁢ i / 6 ⁢ W ⁢ ( 3 8 ⁢ π ⁢ ( 4 ⁢ k - 3 ) + 3 4 ⁢ i ⁢ ln ⁡ 2 ) . Airy-Bi complex-zero-derivative-Airy-Bi 𝑘 superscript 1 𝑘 1 2 superscript 𝑒 𝜋 𝑖 6 𝑊 3 8 𝜋 4 𝑘 3 3 4 𝑖 2 {\displaystyle{\displaystyle\mathrm{Bi}\left(\beta^{\prime}_{k}\right)=(-1)^{k% -1}\sqrt{2}e^{\pi i/6}W\left(\tfrac{3}{8}\pi(4k-3)+\tfrac{3}{4}i\ln 2\right).}}
    0 references
    DLMF id
    DLMF:9.9.E17
    0 references
    Symbols used
    Q11081
    Defining formula
    Bi ⁡ ( z ) Airy-Bi 𝑧 {\displaystyle{\displaystyle\mathrm{Bi}\left(\NVar{z}\right)}}
    xml-id
    C9.S2.SS1.m2aedec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aodec
    0 references
    Q11399
    Defining formula
    β k ′ complex-zero-derivative-Airy-Bi 𝑘 {\displaystyle{\displaystyle\beta^{\prime}_{\NVar{k}}}}
    xml-id
    C9.S9.SS1.p2.m10aadec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2acdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2acdec
    0 references
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2acdec
    0 references
    Q11385
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C9.S1.XMD1.m1pdec
    0 references
    expansion (locally)
    Defining formula
    W 𝑊 {\displaystyle{\displaystyle W}}
    xml-id
    C9.S9.XMD5.m1bdec
    0 references
     
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