DLMF:6.7.E6 (Q2259)

From testwiki
Revision as of 01:27, 2 January 2020 by imported>Admin (Admin moved page Main Page to Verifying DLMF with Maple and Mathematica)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:6.7.E6
No description defined

    Statements

    test
    ∫ x ∞ t ⁢ e - t a 2 + t 2 ⁢ d t = 1 2 ⁢ ( e i ⁢ a ⁢ E 1 ⁡ ( x + i ⁢ a ) + e - i ⁢ a ⁢ E 1 ⁡ ( x - i ⁢ a ) ) , superscript subscript 𝑥 𝑡 superscript 𝑒 𝑡 superscript 𝑎 2 superscript 𝑡 2 𝑡 1 2 superscript 𝑒 𝑖 𝑎 exponential-integral 𝑥 𝑖 𝑎 superscript 𝑒 𝑖 𝑎 exponential-integral 𝑥 𝑖 𝑎 {\displaystyle{\displaystyle\int_{x}^{\infty}\frac{te^{-t}}{a^{2}+t^{2}}% \mathrm{d}t=\tfrac{1}{2}\left(e^{ia}E_{1}\left(x+ia\right)+e^{-ia}E_{1}\left(x% -ia\right)\right),}}
    0 references
    DLMF id
    DLMF:6.7.E6
    0 references
    constraint
    x ∈ ℝ 𝑥 {\displaystyle{\displaystyle x\in\mathbb{R}}}
    0 references
    a > 0 𝑎 0 {\displaystyle{\displaystyle a>0}}
    0 references
    x ∈ ℝ 𝑥 ℝ {\displaystyle{\displaystyle x\in\mathbb{R}}}
    0 references
    Symbols used
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aedec
    0 references
    Q10784
    test
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2aadec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aedec
    0 references
    exponential integral
    test
    E 1 ⁡ ( z ) exponential-integral 𝑧 {\displaystyle{\displaystyle E_{1}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E1.m2addec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2addec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aedec
    0 references
    Q10812
    test
    ℝ {\displaystyle{\displaystyle\mathbb{R}}}
    xml-id
    introduction.Sx4.p2.t1.r14.m2aadec
    0 references
    Q11307
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C6.S1.XMD1.m1ddec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q2259&oldid=11107"