DLMF:6.7.E11 (Q2264): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10784 / rank
 
Normal rank
Property / Symbols used: Q10784 / qualifier
 
test:

∈ {\displaystyle{\displaystyle\in}}

\in
Property / Symbols used: Q10784 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r10.m2addec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
test:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2ajdec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
test:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2agdec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
test:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3ajdec
Property / Symbols used
 
Property / Symbols used: Q10811 / rank
 
Normal rank
Property / Symbols used: Q10811 / qualifier
 
test:

ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}

\realpart@@
Property / Symbols used: Q10811 / qualifier
 
xml-id: C1.S9.E2.m1aadec
Property / Symbols used
 
Property / Symbols used: Q10812 / rank
 
Normal rank
Property / Symbols used: Q10812 / qualifier
 
test:

ℝ {\displaystyle{\displaystyle\mathbb{R}}}

\Reals
Property / Symbols used: Q10812 / qualifier
 
xml-id: introduction.Sx4.p2.t1.r14.m2addec

Latest revision as of 00:28, 2 January 2020

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English
DLMF:6.7.E11
No description defined

    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
    0 references
    constraint
    a , b ∈ ℝ 𝑎 𝑏 {\displaystyle{\displaystyle a,b\in\mathbb{R}}}
    0 references
    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
    0 references
    cosine function
    test
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2acdec
    0 references
    cosine integral
    test
    Cin ⁡ ( z ) cosine-integral-Cin 𝑧 {\displaystyle{\displaystyle\mathrm{Cin}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E12.m2aadec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ajdec
    0 references
    Q10784
    test
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2addec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2ajdec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2agdec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3ajdec
    0 references
    Q10811
    test
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1aadec
    0 references
    Q10812
    test
    ℝ {\displaystyle{\displaystyle\mathbb{R}}}
    xml-id
    introduction.Sx4.p2.t1.r14.m2addec
    0 references
     
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