DLMF:6.7.E5 (Q2258): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q10784 / rank
 
Normal rank
Property / Symbols used: Q10784 / qualifier
 
Defining formula:

∈ {\displaystyle{\displaystyle\in}}

\in
Property / Symbols used: Q10784 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r10.m2adec

Revision as of 01:26, 2 January 2020

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DLMF:6.7.E5
No description defined

    Statements

    Defining formula
    ∫ x ∞ e - t a 2 + t 2 ⁢ d t = - 1 2 ⁢ a ⁢ i ⁢ ( e i ⁢ a ⁢ E 1 ⁡ ( x + i ⁢ a ) - e - i ⁢ a ⁢ E 1 ⁡ ( x - i ⁢ a ) ) , superscript subscript 𝑥 superscript 𝑒 𝑡 superscript 𝑎 2 superscript 𝑡 2 𝑡 1 2 𝑎 𝑖 superscript 𝑒 𝑖 𝑎 exponential-integral 𝑥 𝑖 𝑎 superscript 𝑒 𝑖 𝑎 exponential-integral 𝑥 𝑖 𝑎 {\displaystyle{\displaystyle\int_{x}^{\infty}\frac{e^{-t}}{a^{2}+t^{2}}\mathrm% {d}t=-\frac{1}{2ai}\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.E5
    0 references
    constraint
    x ∈ ℝ 𝑥 {\displaystyle{\displaystyle x\in\mathbb{R}}}
    0 references
    a > 0 𝑎 0 {\displaystyle{\displaystyle a>0}}
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    x ∈ ℝ 𝑥 ℝ {\displaystyle{\displaystyle x\in\mathbb{R}}}
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    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1addec
    0 references
    Q10784
    Defining formula
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2adec
    0 references
     
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