DLMF:9.9.E14 (Q2875): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
Defining formula:

ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}

\ln@@{\NVar{z}}
Property / Symbols used: principal branch of logarithm function / qualifier
 
xml-id: C4.S2.E2.m2adec

Revision as of 14:42, 2 January 2020

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DLMF:9.9.E14
No description defined

    Statements

    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),}}
    0 references
    DLMF id
    DLMF:9.9.E14
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aldec
    0 references
    Q11398
    Defining formula
    β k complex-zero-Airy-Bi 𝑘 {\displaystyle{\displaystyle\beta_{\NVar{k}}}}
    xml-id
    C9.S9.SS1.p2.m7adec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2adec
    0 references
     
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