DLMF:6.7.E8 (Q2261)

From DRMF
Revision as of 01:27, 2 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:6.7.E8
No description defined

    Statements

    Defining formula
    ∫ 0 1 e - a ⁢ t ⁢ ( 1 - cos ⁡ ( b ⁢ t ) ) t ⁢ d t = ℜ ⁡ Ein ⁡ ( a + i ⁢ b ) - Ein ⁡ ( a ) , superscript subscript 0 1 superscript 𝑒 𝑎 𝑡 1 𝑏 𝑡 𝑡 𝑡 complementary-exponential-integral 𝑎 𝑖 𝑏 complementary-exponential-integral 𝑎 {\displaystyle{\displaystyle\int_{0}^{1}\frac{e^{-at}(1-\cos\left(bt\right))}{% t}\mathrm{d}t=\Re\mathrm{Ein}\left(a+ib\right)-\mathrm{Ein}\left(a\right),}}
    0 references
    DLMF id
    DLMF:6.7.E8
    0 references
    constraint
    a , b ∈ ℝ 𝑎 𝑏 {\displaystyle{\displaystyle a,b\in\mathbb{R}}}
    0 references
    Symbols used
    complementary exponential integral
    Defining formula
    Ein ⁡ ( z ) complementary-exponential-integral 𝑧 {\displaystyle{\displaystyle\mathrm{Ein}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E3.m2aadec
    0 references
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2adec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1agdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q2261&oldid=31646"