DLMF:32.11.E23 (Q9458): 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.m2akdec
Property / Symbols used
 
Property / Symbols used: Q10817 / rank
 
Normal rank
Property / Symbols used: Q10817 / qualifier
 
Defining formula:

ph phase {\displaystyle{\displaystyle\operatorname{ph}}}

\phase
Property / Symbols used: Q10817 / qualifier
 
xml-id: C1.S9.E7.m1acdec
Property / Symbols used
 
Property / Symbols used: Q12642 / rank
 
Normal rank
Property / Symbols used: Q12642 / qualifier
 
Defining formula:

ρ 𝜌 {\displaystyle{\displaystyle\rho}}

\rho
Property / Symbols used: Q12642 / qualifier
 
xml-id: C32.S11.XMD12.m1cdec
Property / Symbols used
 
Property / Symbols used: Q12643 / rank
 
Normal rank
Property / Symbols used: Q12643 / qualifier
 
Defining formula:

θ 𝜃 {\displaystyle{\displaystyle\theta}}

\theta
Property / Symbols used: Q12643 / qualifier
 
xml-id: C32.S11.XMD13.m1adec
Property / Symbols used
 
Property / Symbols used: DLMF:32.11.E24 / rank
 
Normal rank
Property / Symbols used: DLMF:32.11.E24 / qualifier
 
Defining formula:

s 𝑠 {\displaystyle{\displaystyle s}}

s
Property / Symbols used: DLMF:32.11.E24 / qualifier
 
xml-id: C32.S11.XMD15.m1bdec

Latest revision as of 14:16, 2 January 2020

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English
DLMF:32.11.E23
No description defined

    Statements

    Defining formula
    θ = - 3 4 ⁢ π - 7 2 ⁢ ρ 2 ⁢ ln ⁡ 2 + ph ⁡ ( 1 + s 2 ) + ph ⁡ Γ ⁡ ( i ⁢ ρ 2 ) , 𝜃 3 4 𝜋 7 2 superscript 𝜌 2 2 phase 1 superscript 𝑠 2 phase Euler-Gamma 𝑖 superscript 𝜌 2 {\displaystyle{\displaystyle\theta=-\tfrac{3}{4}\pi-\tfrac{7}{2}\rho^{2}\ln{2}% +\operatorname{ph}\left(1+s^{2}\right)+\operatorname{ph}\Gamma\left(i\rho^{2}% \right),}}
    0 references
    DLMF id
    DLMF:32.11.E23
    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.m2acdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2afdec
    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.m2akdec
    0 references
    Q10817
    Defining formula
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1acdec
    0 references
    Q12642
    Defining formula
    ρ 𝜌 {\displaystyle{\displaystyle\rho}}
    xml-id
    C32.S11.XMD12.m1cdec
    0 references
    Q12643
    Defining formula
    θ 𝜃 {\displaystyle{\displaystyle\theta}}
    xml-id
    C32.S11.XMD13.m1adec
    0 references
    DLMF:32.11.E24
    Defining formula
    s 𝑠 {\displaystyle{\displaystyle s}}
    xml-id
    C32.S11.XMD15.m1bdec
    0 references
     
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