DLMF:2.4.E6 (Q759)

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DLMF:2.4.E6
No description defined

    Statements

    Defining formula
    f ⁢ ( t ) = 1 2 ⁢ π ⁢ i ⁢ lim η → ∞ ⁡ ∫ σ - i ⁢ η σ + i ⁢ η e t ⁢ z ⁢ F ⁢ ( z ) ⁢ d z 𝑓 𝑡 1 2 𝜋 𝑖 subscript → 𝜂 superscript subscript 𝜎 𝑖 𝜂 𝜎 𝑖 𝜂 superscript 𝑒 𝑡 𝑧 𝐹 𝑧 𝑧 {\displaystyle{\displaystyle f(t)=\frac{1}{2\pi i}\lim\limits_{\eta\to\infty}% \int_{\sigma-i\eta}^{\sigma+i\eta}e^{tz}F(z)\mathrm{d}z}}
    0 references
    DLMF id
    DLMF:2.4.E6
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1addec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2addec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2abdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3addec
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    Q10976
    Defining formula
    σ 𝜎 {\displaystyle{\displaystyle\sigma}}
    xml-id
    C2.S4.XMD7.m1bdec
    0 references
    Q10977
    Defining formula
    F ⁢ ( z ) 𝐹 𝑧 {\displaystyle{\displaystyle F(z)}}
    xml-id
    C2.S4.XMD8.m1dec
    0 references
    Q10978
    Defining formula
    f ⁢ ( x ) 𝑓 𝑥 {\displaystyle{\displaystyle f(x)}}
    xml-id
    C2.S4.XMD9.m1dec
    0 references
     
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