DLMF:6.14.E1 (Q2299): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
Defining formula:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3adec

Revision as of 01:33, 2 January 2020

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DLMF:6.14.E1
No description defined

    Statements

    Defining formula
    ∫ 0 ∞ e - a ⁢ t ⁢ E 1 ⁡ ( t ) ⁢ d t = 1 a ⁢ ln ⁡ ( 1 + a ) , superscript subscript 0 superscript 𝑒 𝑎 𝑡 exponential-integral 𝑡 𝑡 1 𝑎 1 𝑎 {\displaystyle{\displaystyle\int_{0}^{\infty}e^{-at}E_{1}\left(t\right)\mathrm% {d}t=\frac{1}{a}\ln\left(1+a\right),}}
    0 references
    DLMF id
    DLMF:6.14.E1
    0 references
    constraint
    ℜ ⁡ a > - 1 𝑎 1 {\displaystyle{\displaystyle\Re a>-1}}
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    exponential integral
    Defining formula
    E 1 ⁡ ( z ) exponential-integral 𝑧 {\displaystyle{\displaystyle E_{1}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E1.m2adec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
    0 references
     
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