DLMF:7.7.E15 (Q2385)

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DLMF:7.7.E15
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    Statements

    Defining formula
    ∫ 0 ∞ e - a ⁢ t ⁢ cos ⁡ ( t 2 ) ⁢ d t = π 2 ⁢ f ⁡ ( a 2 ⁢ π ) , superscript subscript 0 superscript 𝑒 𝑎 𝑡 superscript 𝑡 2 𝑡 𝜋 2 Fresnel-auxilliary-function-f 𝑎 2 𝜋 {\displaystyle{\displaystyle\int_{0}^{\infty}e^{-at}\cos\left(t^{2}\right)% \mathrm{d}t=\sqrt{\frac{\pi}{2}}\mathrm{f}\left(\frac{a}{\sqrt{2\pi}}\right),}}
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    DLMF id
    DLMF:7.7.E15
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