DLMF:6.7.E15 (Q2268)

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DLMF:6.7.E15
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    Statements

    Defining formula
    f ⁡ ( z ) = 2 ⁢ ∫ 0 ∞ K 0 ⁡ ( 2 ⁢ z ⁢ t ) ⁢ cos ⁡ t ⁢ d t , sine-cosine-integral-f 𝑧 2 superscript subscript 0 modified-Bessel-second-kind 0 2 𝑧 𝑡 𝑡 𝑡 {\displaystyle{\displaystyle\mathrm{f}\left(z\right)=2\int_{0}^{\infty}K_{0}% \left(2\sqrt{zt}\right)\cos t\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:6.7.E15
    0 references
    Symbols used
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aedec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1andec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3andec
    0 references
    modified Bessel function of the second kind
    Defining formula
    K ν ⁡ ( z ) modified-Bessel-second-kind 𝜈 𝑧 {\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S25.E3.m2adec
    0 references
    auxiliary function for sine and cosine integrals
    Defining formula
    f ⁡ ( z ) sine-cosine-integral-f 𝑧 {\displaystyle{\displaystyle\mathrm{f}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E17.m2abdec
    0 references
    Q11305
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C6.S1.XMD2.m1edec
    0 references
     
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