2.5.E33 (Q779)

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2.5.E33
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    Statements

    DLMF defining formula
    I j ⁢ k ⁢ ( x ) = 1 2 ⁢ π ⁢ i ⁢ ∫ p j ⁢ k - i ⁢ ∞ p j ⁢ k + i ⁢ ∞ x - z ⁢ G j ⁢ k ⁢ ( z ) ⁢ d z . subscript 𝐼 𝑗 𝑘 𝑥 1 2 𝜋 𝑖 superscript subscript subscript 𝑝 𝑗 𝑘 𝑖 subscript 𝑝 𝑗 𝑘 𝑖 superscript 𝑥 𝑧 subscript 𝐺 𝑗 𝑘 𝑧 𝑧 {\displaystyle{\displaystyle I_{jk}(x)=\frac{1}{2\pi i}\int_{p_{jk}-i\infty}^{% p_{jk}+i\infty}x^{-z}G_{jk}(z)\mathrm{d}z.}}
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2afdec
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    differential of x
    DLMF defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1agdec
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    imaginary unit
    DLMF defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aedec
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    integral
    DLMF defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3agdec
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    function
    DLMF defining formula
    G j ⁢ k ⁢ ( z ) subscript 𝐺 𝑗 𝑘 𝑧 {\displaystyle{\displaystyle G_{jk}(z)}}
    xml-id
    C2.S5.XMD21.m1adec
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    real number
    DLMF defining formula
    p j ⁢ k subscript 𝑝 𝑗 𝑘 {\displaystyle{\displaystyle p_{jk}}}
    xml-id
    C2.S5.XMD22.m1dec
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    convolution integral
    DLMF defining formula
    I ⁢ ( x ) 𝐼 𝑥 {\displaystyle{\displaystyle I(x)}}
    xml-id
    C2.S5.XMD5.m1jdec
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    Identifiers

     
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