DLMF:7.19.E11 (Q2478)

From DRMF
Revision as of 13:35, 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:7.19.E11
No description defined

    Statements

    Defining formula
    𝖵 ⁡ ( u a , 1 4 ⁢ a 2 ) = a ⁢ ∫ 0 ∞ e - a ⁢ t - 1 4 ⁢ t 2 ⁢ sin ⁡ ( u ⁢ t ) ⁢ d t . Voigt-V 𝑢 𝑎 1 4 superscript 𝑎 2 𝑎 superscript subscript 0 superscript 𝑒 𝑎 𝑡 1 4 superscript 𝑡 2 𝑢 𝑡 𝑡 {\displaystyle{\displaystyle\mathsf{V}\left(\frac{u}{a},\frac{1}{4a^{2}}\right% )=a\int_{0}^{\infty}e^{-at-\frac{1}{4}t^{2}}\sin\left(ut\right)\mathrm{d}t.}}
    0 references
    DLMF id
    DLMF:7.19.E11
    0 references
    Symbols used
    Voigt function
    Defining formula
    𝖵 ⁡ ( x , t ) Voigt-V 𝑥 𝑡 {\displaystyle{\displaystyle\mathsf{V}\left(\NVar{x},\NVar{t}\right)}}
    xml-id
    C7.S19.E2.m2ahdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1addec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aedec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3addec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q2478&oldid=37900"