DLMF:32.11.E36 (Q9471): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12648 / rank
 
Normal rank
Property / Symbols used: Q12648 / qualifier
 
Defining formula:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q12648 / qualifier
 
xml-id: C32.S11.XMD19.m1bdec

Revision as of 14:18, 2 January 2020

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DLMF:32.11.E36
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    Statements

    Defining formula
    θ 0 = 1 3 ⁢ d 2 ⁢ 3 ⁢ ln ⁡ 3 + 2 3 ⁢ π ⁢ ν + 7 12 ⁢ π + ph ⁡ μ + ph ⁡ Γ ⁡ ( - 2 3 ⁢ i ⁢ 3 ⁢ d 2 ) , subscript 𝜃 0 1 3 superscript 𝑑 2 3 3 2 3 𝜋 𝜈 7 12 𝜋 phase 𝜇 phase Euler-Gamma 2 3 𝑖 3 superscript 𝑑 2 {\displaystyle{\displaystyle\theta_{0}=\tfrac{1}{3}d^{2}\sqrt{3}\ln 3+\tfrac{2% }{3}\pi\nu+\tfrac{7}{12}\pi+\operatorname{ph}\mu+\operatorname{ph}\Gamma\left(% -\tfrac{2}{3}i\sqrt{3}d^{2}\right),}}
    0 references
    DLMF id
    DLMF:32.11.E36
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2ahdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2akdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aedec
    0 references
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2aodec
    0 references
    Q10817
    Defining formula
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1aedec
    0 references
    Q12648
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C32.S11.XMD19.m1bdec
    0 references
     
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