DLMF:9.13.E23 (Q2987)

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DLMF:9.13.E23
No description defined

    Statements

    Defining formula
    U 1 ⁢ ( x , α ) = π 1 / 2 2 ( m + 2 ) / ( 2 ⁢ m ) ⁢ Γ ⁡ ( 1 / m ) ⁢ ( W m ⁢ ( t ) + W m ⁢ ( - t ) ) , subscript 𝑈 1 𝑥 𝛼 superscript 𝜋 1 2 superscript 2 𝑚 2 2 𝑚 Euler-Gamma 1 𝑚 subscript 𝑊 𝑚 𝑡 subscript 𝑊 𝑚 𝑡 {\displaystyle{\displaystyle U_{1}(x,\alpha)=\frac{\pi^{1/2}}{2^{(m+2)/(2m)}% \Gamma\left(1/m\right)}\left(W_{m}(t)+W_{m}(-t)\right),}}
    0 references
    DLMF id
    DLMF:9.13.E23
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    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2acdec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aidec
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    parameter (locally)
    Defining formula
    α 𝛼 {\displaystyle{\displaystyle\alpha}}
    xml-id
    C9.S13.XMD10.m1ddec
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    parameter (locally)
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C9.S13.XMD11.m1ddec
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    Q11419
    Defining formula
    U i subscript 𝑈 𝑖 {\displaystyle{\displaystyle U_{i}}}
    xml-id
    C9.S13.XMD12.m1edec
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    Q11418
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C9.S13.XMD5.m1gdec
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    function (locally)
    Defining formula
    W m subscript 𝑊 𝑚 {\displaystyle{\displaystyle W_{m}}}
    xml-id
    C9.S13.XMD8.m1adec
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