DLMF:32.11.E9 (Q9444): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
Defining formula:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2aadec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
Defining formula:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2adec
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.m2acdec
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.m1adec
Property / Symbols used
 
Property / Symbols used: Q10897 / rank
 
Normal rank
Property / Symbols used: Q10897 / qualifier
 
Defining formula:

sign ⁡ x sign 𝑥 {\displaystyle{\displaystyle\operatorname{sign}\NVar{x}}}

\sign@@{\NVar{x}}
Property / Symbols used: Q10897 / qualifier
 
xml-id: introduction.Sx4.p2.t1.r18.m6adec
Property / Symbols used
 
Property / Symbols used: Q12534 / rank
 
Normal rank
Property / Symbols used: Q12534 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q12534 / qualifier
 
xml-id: C32.S1.XMD5.m1bdec
Property / Symbols used
 
Property / Symbols used: Q12635 / rank
 
Normal rank
Property / Symbols used: Q12635 / qualifier
 
Defining formula:

d 𝑑 {\displaystyle{\displaystyle d}}

d
Property / Symbols used: Q12635 / qualifier
 
xml-id: C32.S11.XMD5.m1cdec
Property / Symbols used
 
Property / Symbols used: Q12636 / rank
 
Normal rank
Property / Symbols used: Q12636 / qualifier
 
Defining formula:

θ 0 subscript 𝜃 0 {\displaystyle{\displaystyle\theta_{0}}}

\theta_{0}
Property / Symbols used: Q12636 / qualifier
 
xml-id: C32.S11.XMD6.m1adec

Latest revision as of 14:13, 2 January 2020

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DLMF:32.11.E9
No description defined

    Statements

    Defining formula
    θ 0 = 3 2 ⁢ d 2 ⁢ ln ⁡ 2 + ph ⁡ Γ ⁡ ( 1 - 1 2 ⁢ i ⁢ d 2 ) + 1 4 ⁢ π ⁢ ( 1 - 2 ⁢ sign ⁡ ( k ) ) , subscript 𝜃 0 3 2 superscript 𝑑 2 2 phase Euler-Gamma 1 1 2 𝑖 superscript 𝑑 2 1 4 𝜋 1 2 sign 𝑘 {\displaystyle{\displaystyle\theta_{0}=\tfrac{3}{2}d^{2}\ln 2+\operatorname{ph% }\Gamma\left(1-\tfrac{1}{2}id^{2}\right)+\tfrac{1}{4}\pi(1-2\operatorname{sign% }\left(k\right)),}}
    0 references
    DLMF id
    DLMF:32.11.E9
    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.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    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.m2acdec
    0 references
    Q10817
    Defining formula
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1adec
    0 references
    Q10897
    Defining formula
    sign ⁡ x sign 𝑥 {\displaystyle{\displaystyle\operatorname{sign}\NVar{x}}}
    xml-id
    introduction.Sx4.p2.t1.r18.m6adec
    0 references
    Q12534
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C32.S1.XMD5.m1bdec
    0 references
    Q12635
    Defining formula
    d 𝑑 {\displaystyle{\displaystyle d}}
    xml-id
    C32.S11.XMD5.m1cdec
    0 references
    Q12636
    Defining formula
    θ 0 subscript 𝜃 0 {\displaystyle{\displaystyle\theta_{0}}}
    xml-id
    C32.S11.XMD6.m1adec
    0 references
     
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