DLMF:7.19.E4 (Q2468)

From DRMF
Revision as of 13:34, 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.E4
No description defined

    Statements

    Defining formula
    H ⁡ ( a , u ) = a π ⁢ ∫ - ∞ ∞ e - t 2 ⁢ d t ( u - t ) 2 + a 2 = 1 a ⁢ π ⁢ 𝖴 ⁡ ( u a , 1 4 ⁢ a 2 ) . line-broadening-function 𝑎 𝑢 𝑎 𝜋 superscript subscript superscript 𝑒 superscript 𝑡 2 𝑡 superscript 𝑢 𝑡 2 superscript 𝑎 2 1 𝑎 𝜋 Voigt-U 𝑢 𝑎 1 4 superscript 𝑎 2 {\displaystyle{\displaystyle H\left(a,u\right)=\frac{a}{\pi}\int_{-\infty}^{% \infty}\frac{e^{-t^{2}}\mathrm{d}t}{(u-t)^{2}+a^{2}}=\frac{1}{a\sqrt{\pi}}% \mathsf{U}\left(\frac{u}{a},\frac{1}{4a^{2}}\right).}}
    0 references
    DLMF id
    DLMF:7.19.E4
    0 references
    Symbols used
    Voigt function
    Defining formula
    𝖴 ⁡ ( x , t ) Voigt-U 𝑥 𝑡 {\displaystyle{\displaystyle\mathsf{U}\left(\NVar{x},\NVar{t}\right)}}
    xml-id
    C7.S19.E1.m2abdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1abdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2acdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q2468&oldid=37786"