DLMF:32.11.E37 (Q9472): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: gamma function / rank
 
Normal rank
Property / Symbols used: gamma function / qualifier
 
Defining formula:

Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

\EulerGamma@{\NVar{z}}
Property / Symbols used: gamma function / qualifier
 
xml-id: C5.S2.E1.m2aidec
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.m2aldec
Property / Symbols used
 
Property / Symbols used: exponential function / rank
 
Normal rank
Property / Symbols used: exponential function / qualifier
 
Defining formula:

exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}

\exp@@{\NVar{z}}
Property / Symbols used: exponential function / qualifier
 
xml-id: C4.S2.E19.m2abdec
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.m2afdec
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.m1cdec
Property / Symbols used
 
Property / Symbols used: Q12652 / rank
 
Normal rank
Property / Symbols used: Q12652 / qualifier
 
Defining formula:

μ 𝜇 {\displaystyle{\displaystyle\mu}}

\mu
Property / Symbols used: Q12652 / qualifier
 
xml-id: C32.S11.XMD24.m1bdec

Latest revision as of 14:18, 2 January 2020

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DLMF:32.11.E37
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    Statements

    Defining formula
    μ = 1 + ( 2 ⁢ i ⁢ h ⁢ π 3 / 2 ⁢ exp ⁡ ( - i ⁢ π ⁢ ν ) / Γ ⁡ ( - ν ) ) , 𝜇 1 2 𝑖 ℎ superscript 𝜋 3 2 𝑖 𝜋 𝜈 Euler-Gamma 𝜈 {\displaystyle{\displaystyle\mu=1+\left(\ifrac{2ih\pi^{3/2}\exp\left(-i\pi\nu% \right)}{\Gamma\left(-\nu\right)}\right),}}
    0 references
    DLMF id
    DLMF:32.11.E37
    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.m2aidec
    0 references
    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
    exponential function
    Defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2abdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2afdec
    0 references
    Q12648
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C32.S11.XMD19.m1cdec
    0 references
    Q12652
    Defining formula
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    xml-id
    C32.S11.XMD24.m1bdec
    0 references
     
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