DLMF:6.2.E5 (Q2215): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
Defining formula:

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

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1acdec
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.m2acdec
Property / Symbols used
 
Property / Symbols used: Q11306 / rank
 
Normal rank
Property / Symbols used: Q11306 / qualifier
 
Defining formula:

Ei ⁡ ( x ) exponential-integral-Ei 𝑥 {\displaystyle{\displaystyle\mathrm{Ei}\left(\NVar{x}\right)}}

\expintEi@{\NVar{x}}
Property / Symbols used: Q11306 / qualifier
 
xml-id: C6.S2.SS1.p3.m2adec
Property / Symbols used
 
Property / Symbols used: Cauchy principal value / rank
 
Normal rank
Property / Symbols used: Cauchy principal value / qualifier
 
Defining formula:

⨍ a b superscript subscript principal-value-integral 𝑎 𝑏 {\displaystyle{\displaystyle\pvint_{\NVar{a}}^{\NVar{b}}}}

\pvint_{\NVar{a}}^{\NVar{b}}
Property / Symbols used: Cauchy principal value / qualifier
 
xml-id: C1.S4.E24.m2adec
Property / Symbols used
 
Property / Symbols used: Q11307 / rank
 
Normal rank
Property / Symbols used: Q11307 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11307 / qualifier
 
xml-id: C6.S1.XMD1.m1dec

Latest revision as of 01:13, 2 January 2020

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DLMF:6.2.E5
No description defined

    Statements

    Defining formula
    Ei ⁡ ( x ) = - ⨍ - x ∞ e - t t ⁢ d t = ⨍ - ∞ x e t t ⁢ d t , exponential-integral-Ei 𝑥 superscript subscript principal-value-integral 𝑥 superscript 𝑒 𝑡 𝑡 𝑡 superscript subscript principal-value-integral 𝑥 superscript 𝑒 𝑡 𝑡 𝑡 {\displaystyle{\displaystyle\mathrm{Ei}\left(x\right)=-\,\pvint_{-x}^{\infty}% \frac{e^{-t}}{t}\mathrm{d}t=\pvint_{-\infty}^{x}\frac{e^{t}}{t}\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:6.2.E5
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1acdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2acdec
    0 references
    Q11306
    Defining formula
    Ei ⁡ ( x ) exponential-integral-Ei 𝑥 {\displaystyle{\displaystyle\mathrm{Ei}\left(\NVar{x}\right)}}
    xml-id
    C6.S2.SS1.p3.m2adec
    0 references
    Cauchy principal value
    Defining formula
    ⨍ a b superscript subscript principal-value-integral 𝑎 𝑏 {\displaystyle{\displaystyle\pvint_{\NVar{a}}^{\NVar{b}}}}
    xml-id
    C1.S4.E24.m2adec
    0 references
    Q11307
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C6.S1.XMD1.m1dec
    0 references
     
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