DLMF:6.7.E7 (Q2260): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: complementary exponential integral / rank
 
Normal rank
Property / Symbols used: complementary exponential integral / qualifier
 
Defining formula:

Ein ⁡ ( z ) complementary-exponential-integral 𝑧 {\displaystyle{\displaystyle\mathrm{Ein}\left(\NVar{z}\right)}}

\expintEin@{\NVar{z}}
Property / Symbols used: complementary exponential integral / qualifier
 
xml-id: C6.S2.E3.m2adec

Revision as of 01:27, 2 January 2020

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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),}}
    0 references
    DLMF id
    DLMF:6.7.E7
    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.m2adec
    0 references
     
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