DLMF:6.7.E7 (Q2260)

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DLMF:6.7.E7
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    Statements

    Defining formula
    ∫ 0 1 e - a ⁢ t ⁢ sin ⁡ ( b ⁢ t ) t ⁢ d t = ℑ ⁡ Ein ⁡ ( a + i ⁢ b ) , superscript subscript 0 1 superscript 𝑒 𝑎 𝑡 𝑏 𝑡 𝑡 𝑡 complementary-exponential-integral 𝑎 𝑖 𝑏 {\displaystyle{\displaystyle\int_{0}^{1}\frac{e^{-at}\sin\left(bt\right)}{t}% \mathrm{d}t=\Im\mathrm{Ein}\left(a+ib\right),}}
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    DLMF id
    DLMF:6.7.E7
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    constraint
    a , b ∈ ℝ 𝑎 𝑏 {\displaystyle{\displaystyle a,b\in\mathbb{R}}}
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    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.m2adec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1afdec
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    Q10784
    Defining formula
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2abdec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2afdec
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