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3.5.E39 - MaRDI portal

3.5.E39 (Q1265)

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3.5.E39
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    Statements

    DLMF defining formula
    g ⁢ ( t ) = 1 2 ⁢ π ⁢ i ⁢ ∫ σ - i ⁢ ∞ σ + i ⁢ ∞ e t ⁢ p ⁢ G ⁢ ( p ) ⁢ d p , 𝑔 𝑡 1 2 imaginary-unit superscript subscript 𝜎 imaginary-unit 𝜎 imaginary-unit superscript 𝑒 𝑡 𝑝 𝐺 𝑝 𝑝 {\displaystyle{\displaystyle g(t)=\frac{1}{2\pi\mathrm{i}}\int_{\sigma-\mathrm% {i}\infty}^{\sigma+\mathrm{i}\infty}e^{tp}G(p)\mathrm{d}p,}}
    0 references
    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.m2agdec
    0 references
    differential of x
    DLMF defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1andec
    0 references
    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2afdec
    0 references
    imaginary unit
    DLMF defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2acdec
    0 references
    integral
    DLMF defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3andec
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    function
    DLMF defining formula
    g ⁢ ( t ) 𝑔 𝑡 {\displaystyle{\displaystyle g(t)}}
    xml-id
    C3.S5.XMD18.m1adec
    0 references
    Laplace transform of $$g(t)$$ (locally)
    DLMF defining formula
    G ⁢ ( p ) 𝐺 𝑝 {\displaystyle{\displaystyle G(p)}}
    xml-id
    C3.S5.XMD19.m1adec
    0 references
    parameter
    DLMF defining formula
    σ 𝜎 {\displaystyle{\displaystyle\sigma}}
    xml-id
    C3.S5.XMD20.m1dec
    0 references

    Identifiers

     
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