DLMF:9.13.E24 (Q2988)

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DLMF:9.13.E24
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    Statements

    test
    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).}}
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    DLMF id
    DLMF:9.13.E24
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    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2addec
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    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ajdec
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    parameter (locally)
    test
    α 𝛼 {\displaystyle{\displaystyle\alpha}}
    xml-id
    C9.S13.XMD10.m1edec
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    parameter (locally)
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C9.S13.XMD11.m1edec
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    Q11419
    test
    U i subscript 𝑈 𝑖 {\displaystyle{\displaystyle U_{i}}}
    xml-id
    C9.S13.XMD12.m1fdec
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    Q11418
    test
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C9.S13.XMD5.m1hdec
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