DLMF:6.7.E2 (Q2255)

From DRMF
Revision as of 01:26, 2 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:6.7.E2
No description defined

    Statements

    Defining formula
    e x ⁢ ∫ 0 α e - x ⁢ t 1 - t ⁢ d t = Ei ⁡ ( x ) - Ei ⁡ ( ( 1 - α ) ⁢ x ) , superscript 𝑒 𝑥 superscript subscript 0 𝛼 superscript 𝑒 𝑥 𝑡 1 𝑡 𝑡 exponential-integral-Ei 𝑥 exponential-integral-Ei 1 𝛼 𝑥 {\displaystyle{\displaystyle e^{x}\int_{0}^{\alpha}\frac{e^{-xt}}{1-t}\mathrm{% d}t=\mathrm{Ei}\left(x\right)-\mathrm{Ei}\left((1-\alpha)x\right),}}
    0 references
    DLMF id
    DLMF:6.7.E2
    0 references
    constraint
    x > 0 𝑥 0 {\displaystyle{\displaystyle x>0}}
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aadec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    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
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q2255&oldid=31437"