DLMF:2.4.E3 (Q756)

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DLMF:2.4.E3
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    Statements

    test
    q ⁢ ( t ) = 1 2 ⁢ π ⁢ i ⁢ lim η → ∞ ⁡ ∫ σ - i ⁢ η σ + i ⁢ η e t ⁢ z ⁢ Q ⁢ ( z ) ⁢ d z , 𝑞 𝑡 1 2 𝜋 𝑖 subscript → 𝜂 superscript subscript 𝜎 𝑖 𝜂 𝜎 𝑖 𝜂 superscript 𝑒 𝑡 𝑧 𝑄 𝑧 𝑧 {\displaystyle{\displaystyle q(t)=\frac{1}{2\pi i}\lim\limits_{\eta\to\infty}% \int_{\sigma-i\eta}^{\sigma+i\eta}e^{tz}Q(z)\mathrm{d}z,}}
    0 references
    DLMF id
    DLMF:2.4.E3
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    constraint
    0 < t < ∞ 0 𝑡 {\displaystyle{\displaystyle 0<t<\infty}}
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
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