DLMF:6.7.E11 (Q2264)

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DLMF:6.7.E11
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    Statements

    test
    ∫ 0 1 ( 1 - e - a ⁢ t ) ⁢ cos ⁡ ( b ⁢ t ) t ⁢ d t = ℜ ⁡ Ein ⁡ ( a + i ⁢ b ) - Cin ⁡ ( b ) , superscript subscript 0 1 1 superscript 𝑒 𝑎 𝑡 𝑏 𝑡 𝑡 𝑡 complementary-exponential-integral 𝑎 𝑖 𝑏 cosine-integral-Cin 𝑏 {\displaystyle{\displaystyle\int_{0}^{1}\frac{(1-e^{-at})\cos\left(bt\right)}{% t}\mathrm{d}t=\Re\mathrm{Ein}\left(a+ib\right)-\mathrm{Cin}\left(b\right),}}
    0 references
    DLMF id
    DLMF:6.7.E11
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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
    test
    Ein ⁡ ( z ) complementary-exponential-integral 𝑧 {\displaystyle{\displaystyle\mathrm{Ein}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E3.m2acdec
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    cosine function
    test
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2acdec
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    cosine integral
    test
    Cin ⁡ ( z ) cosine-integral-Cin 𝑧 {\displaystyle{\displaystyle\mathrm{Cin}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E12.m2aadec
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    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ajdec
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    Q10784
    test
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2addec
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    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2ajdec
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    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2agdec
    0 references
     
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