DLMF:7.7.E11 (Q2381)

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DLMF:7.7.E11
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    Statements

    Defining formula
    g ⁡ ( z ) = 1 π ⁢ 2 ⁢ ∫ 0 ∞ t ⁢ e - π ⁢ z 2 ⁢ t / 2 t 2 + 1 ⁢ d t , Fresnel-auxilliary-function-g 𝑧 1 𝜋 2 superscript subscript 0 𝑡 superscript 𝑒 𝜋 superscript 𝑧 2 𝑡 2 superscript 𝑡 2 1 𝑡 {\displaystyle{\displaystyle\mathrm{g}\left(z\right)=\frac{1}{\pi\sqrt{2}}\int% _{0}^{\infty}\frac{\sqrt{t}e^{-\pi z^{2}t/2}}{t^{2}+1}\mathrm{d}t,}}
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    DLMF id
    DLMF:7.7.E11
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    constraint
    | ph ⁡ z | ≤ 1 4 ⁢ π phase 𝑧 1 4 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\frac{1}{4}\pi}}
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