DLMF:6.7.E1 (Q2254): Difference between revisions

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Property / constraint
 

b > 0 𝑏 0 {\displaystyle{\displaystyle b>0}}

b>0
Property / constraint: b > 0 𝑏 0 {\displaystyle{\displaystyle b>0}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1adec
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.m2adec
Property / Symbols used
 
Property / Symbols used: exponential integral / rank
 
Normal rank
Property / Symbols used: exponential integral / qualifier
 
test:

E 1 ⁡ ( z ) exponential-integral 𝑧 {\displaystyle{\displaystyle E_{1}\left(\NVar{z}\right)}}

\expintE@{\NVar{z}}
Property / Symbols used: exponential integral / qualifier
 
xml-id: C6.S2.E1.m2adec
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.m2adec
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.m3adec

Latest revision as of 00:26, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:6.7.E1
No description defined

    Statements

    test
    ∫ 0 ∞ e - a ⁢ t t + b ⁢ d t = ∫ 0 ∞ e i ⁢ a ⁢ t t + i ⁢ b ⁢ d t = e a ⁢ b ⁢ E 1 ⁡ ( a ⁢ b ) , superscript subscript 0 superscript 𝑒 𝑎 𝑡 𝑡 𝑏 𝑡 superscript subscript 0 superscript 𝑒 𝑖 𝑎 𝑡 𝑡 𝑖 𝑏 𝑡 superscript 𝑒 𝑎 𝑏 exponential-integral 𝑎 𝑏 {\displaystyle{\displaystyle\int_{0}^{\infty}\frac{e^{-at}}{t+b}\mathrm{d}t=% \int_{0}^{\infty}\frac{e^{iat}}{t+ib}\mathrm{d}t=e^{ab}E_{1}\left(ab\right),}}
    0 references
    DLMF id
    DLMF:6.7.E1
    0 references
    constraint
    b > 0 𝑏 0 {\displaystyle{\displaystyle b>0}}
    0 references
    Symbols used
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    exponential integral
    test
    E 1 ⁡ ( z ) exponential-integral 𝑧 {\displaystyle{\displaystyle E_{1}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E1.m2adec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
    0 references
     
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