DLMF:9.13.E24 (Q2988): 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.m2addec
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.m2ajdec
Property / Symbols used
 
Property / Symbols used: parameter (locally) / rank
 
Normal rank
Property / Symbols used: parameter (locally) / qualifier
 
Defining formula:

α 𝛼 {\displaystyle{\displaystyle\alpha}}

\alpha
Property / Symbols used: parameter (locally) / qualifier
 
xml-id: C9.S13.XMD10.m1edec
Property / Symbols used
 
Property / Symbols used: parameter (locally) / rank
 
Normal rank
Property / Symbols used: parameter (locally) / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: parameter (locally) / qualifier
 
xml-id: C9.S13.XMD11.m1edec
Property / Symbols used
 
Property / Symbols used: Q11419 / rank
 
Normal rank
Property / Symbols used: Q11419 / qualifier
 
Defining formula:

U i subscript 𝑈 𝑖 {\displaystyle{\displaystyle U_{i}}}

U_{i}
Property / Symbols used: Q11419 / qualifier
 
xml-id: C9.S13.XMD12.m1fdec
Property / Symbols used
 
Property / Symbols used: Q11418 / rank
 
Normal rank
Property / Symbols used: Q11418 / qualifier
 
Defining formula:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q11418 / qualifier
 
xml-id: C9.S13.XMD5.m1hdec
Property / Symbols used
 
Property / Symbols used: function (locally) / rank
 
Normal rank
Property / Symbols used: function (locally) / qualifier
 
Defining formula:

W m subscript 𝑊 𝑚 {\displaystyle{\displaystyle W_{m}}}

W_{m}
Property / Symbols used: function (locally) / qualifier
 
xml-id: C9.S13.XMD8.m1bdec

Latest revision as of 15:02, 2 January 2020

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DLMF:9.13.E24
No description defined

    Statements

    Defining formula
    U 2 ⁢ ( x , α ) = π 1 / 2 ⁢ m 2 / m 2 ( m + 2 ) / ( 2 ⁢ m ) ⁢ Γ ⁡ ( - 1 / m ) ⁢ ( W m ⁢ ( t ) - W m ⁢ ( - t ) ) . subscript 𝑈 2 𝑥 𝛼 superscript 𝜋 1 2 superscript 𝑚 2 𝑚 superscript 2 𝑚 2 2 𝑚 Euler-Gamma 1 𝑚 subscript 𝑊 𝑚 𝑡 subscript 𝑊 𝑚 𝑡 {\displaystyle{\displaystyle U_{2}(x,\alpha)=\frac{\pi^{1/2}m^{2/m}}{2^{(m+2)/% (2m)}\Gamma\left(-1/m\right)}\left(W_{m}(t){-}W_{m}(-t)\right).}}
    0 references
    DLMF id
    DLMF:9.13.E24
    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.m2addec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ajdec
    0 references
    parameter (locally)
    Defining formula
    α 𝛼 {\displaystyle{\displaystyle\alpha}}
    xml-id
    C9.S13.XMD10.m1edec
    0 references
    parameter (locally)
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C9.S13.XMD11.m1edec
    0 references
    Q11419
    Defining formula
    U i subscript 𝑈 𝑖 {\displaystyle{\displaystyle U_{i}}}
    xml-id
    C9.S13.XMD12.m1fdec
    0 references
    Q11418
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C9.S13.XMD5.m1hdec
    0 references
    function (locally)
    Defining formula
    W m subscript 𝑊 𝑚 {\displaystyle{\displaystyle W_{m}}}
    xml-id
    C9.S13.XMD8.m1bdec
    0 references
     
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