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DLMF:6.7.E14 - MaRDI portal

DLMF:6.7.E14 (Q2965)

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DLMF:6.7.E14
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    Statements

    DLMF defining formula
    g ⁡ ( z ) = ∫ 0 ∞ cos ⁡ t t + z ⁢ d t = ∫ 0 ∞ t ⁢ e - z ⁢ t t 2 + 1 ⁢ d t . sine-cosine-integral-g 𝑧 superscript subscript 0 𝑡 𝑡 𝑧 𝑡 superscript subscript 0 𝑡 superscript 𝑒 𝑧 𝑡 superscript 𝑡 2 1 𝑡 {\displaystyle{\displaystyle\mathrm{g}\left(z\right)=\int_{0}^{\infty}\frac{% \cos t}{t+z}\mathrm{d}t=\int_{0}^{\infty}\frac{te^{-zt}}{t^{2}+1}\mathrm{d}t.}}
    0 references
    Symbols used
    cosine function
    DLMF defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2addec
    0 references
    differential of x
    DLMF defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1amdec
    0 references
    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2amdec
    0 references
    integral
    DLMF defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3amdec
    0 references
    auxiliary function for sine and cosine integrals
    DLMF defining formula
    g ⁡ ( z ) sine-cosine-integral-g 𝑧 {\displaystyle{\displaystyle\mathrm{g}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E18.m2aadec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C6.S1.XMD2.m1ddec
    0 references

    Identifiers

     
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