DLMF:2.11.E12 (Q1037)

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DLMF:2.11.E12
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    Statements

    test
    F n + p ⁡ ( z ) = e - z 2 ⁢ π ⁢ ∫ 0 ∞ exp ⁡ ( - ρ ⁢ ( t ⁢ e i ⁢ θ - ln ⁡ t ) ) ⁢ t α - 1 1 + t ⁢ d t . terminant-function 𝑛 𝑝 𝑧 superscript 𝑒 𝑧 2 𝜋 superscript subscript 0 𝜌 𝑡 superscript 𝑒 𝑖 𝜃 𝑡 superscript 𝑡 𝛼 1 1 𝑡 𝑡 {\displaystyle{\displaystyle F_{n+p}\left(z\right)=\frac{e^{-z}}{2\pi}\int_{0}% ^{\infty}\exp\left(-\rho\left(te^{i\theta}-\ln t\right)\right)\frac{t^{\alpha-% 1}}{1+t}\mathrm{d}t.}}
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    DLMF id
    DLMF:2.11.E12
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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.m2aedec
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    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1acdec
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    exponential function
    test
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2adec
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