DLMF:7.19.E10 (Q2477): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
Defining formula:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2addec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
Defining formula:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3acdec

Latest revision as of 13:34, 2 January 2020

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DLMF:7.19.E10
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    Statements

    Defining formula
    𝖴 ⁡ ( u a , 1 4 ⁢ a 2 ) = a ⁢ ∫ 0 ∞ e - a ⁢ t - 1 4 ⁢ t 2 ⁢ cos ⁡ ( u ⁢ t ) ⁢ d t , Voigt-U 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{U}\left(\frac{u}{a},\frac{1}{4a^{2}}\right% )=a\int_{0}^{\infty}e^{-at-\frac{1}{4}t^{2}}\cos\left(ut\right)\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:7.19.E10
    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.m2aidec
    0 references
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2adec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1acdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2addec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3acdec
    0 references
     
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