DLMF:10.43.E18 (Q3632)

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DLMF:10.43.E18
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    Statements

    Defining formula
    ∫ 0 ∞ K ν ⁡ ( t ) ⁢ d t = 1 2 ⁢ π ⁢ sec ⁡ ( 1 2 ⁢ π ⁢ ν ) , superscript subscript 0 modified-Bessel-second-kind 𝜈 𝑡 𝑡 1 2 𝜋 1 2 𝜋 𝜈 {\displaystyle{\displaystyle\int_{0}^{\infty}K_{\nu}\left(t\right)\mathrm{d}t=% \tfrac{1}{2}\pi\sec\left(\tfrac{1}{2}\pi\nu\right),}}
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    DLMF id
    DLMF:10.43.E18
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    constraint
    | ℜ ⁡ ν | < 1 𝜈 1 {\displaystyle{\displaystyle|\Re\nu|<1}}
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