DLMF:6.7.E13 (Q2266)

From DRMF
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:6.7.E13
No description defined

    Statements

    Defining formula
    f ⁡ ( z ) = ∫ 0 ∞ sin ⁡ t t + z ⁢ d t = ∫ 0 ∞ e - z ⁢ t t 2 + 1 ⁢ d t , sine-cosine-integral-f 𝑧 superscript subscript 0 𝑡 𝑡 𝑧 𝑡 superscript subscript 0 superscript 𝑒 𝑧 𝑡 superscript 𝑡 2 1 𝑡 {\displaystyle{\displaystyle\mathrm{f}\left(z\right)=\int_{0}^{\infty}\frac{% \sin t}{t+z}\mathrm{d}t=\int_{0}^{\infty}\frac{e^{-zt}}{t^{2}+1}\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:6.7.E13
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aldec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aldec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aldec
    0 references
    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2acdec
    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.m2aadec
    0 references
    Q11305
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C6.S1.XMD2.m1cdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q2266&oldid=31897"