DLMF:6.14.E2 (Q2300): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
Defining formula:

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

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2aadec

Revision as of 01:33, 2 January 2020

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DLMF:6.14.E2
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    Statements

    Defining formula
    ∫ 0 ∞ e - a ⁢ t ⁢ Ci ⁡ ( t ) ⁢ d t = - 1 2 ⁢ a ⁢ ln ⁡ ( 1 + a 2 ) , superscript subscript 0 superscript 𝑒 𝑎 𝑡 cosine-integral 𝑡 𝑡 1 2 𝑎 1 superscript 𝑎 2 {\displaystyle{\displaystyle\int_{0}^{\infty}e^{-at}\mathrm{Ci}\left(t\right)% \mathrm{d}t=-\frac{1}{2a}\ln\left(1+a^{2}\right),}}
    0 references
    DLMF id
    DLMF:6.14.E2
    0 references
    constraint
    ℜ ⁡ a > 0 𝑎 0 {\displaystyle{\displaystyle\Re a>0}}
    0 references
    Symbols used
    cosine integral
    Defining formula
    Ci ⁡ ( z ) cosine-integral 𝑧 {\displaystyle{\displaystyle\mathrm{Ci}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E11.m2adec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aadec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    0 references
     
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