DLMF:2.4.E7 (Q760)

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DLMF:2.4.E7
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    Statements

    Defining formula
    q ⁢ ( t ) - f ⁢ ( t ) = e σ ⁢ t 2 ⁢ π ⁢ lim η → ∞ ⁡ ∫ - η η e i ⁢ t ⁢ τ ⁢ ( Q ⁢ ( σ + i ⁢ τ ) - F ⁢ ( σ + i ⁢ τ ) ) ⁢ d τ . 𝑞 𝑡 𝑓 𝑡 superscript 𝑒 𝜎 𝑡 2 𝜋 subscript → 𝜂 superscript subscript 𝜂 𝜂 superscript 𝑒 𝑖 𝑡 𝜏 𝑄 𝜎 𝑖 𝜏 𝐹 𝜎 𝑖 𝜏 𝜏 {\displaystyle{\displaystyle q(t)-f(t)=\frac{e^{\sigma t}}{2\pi}\lim\limits_{% \eta\to\infty}\int_{-\eta}^{\eta}e^{it\tau}(Q(\sigma+i\tau)-F(\sigma+i\tau))% \mathrm{d}\tau.}}
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    DLMF id
    DLMF:2.4.E7
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
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