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DLMF:7.19.E3 - MaRDI portal

DLMF:7.19.E3 (Q3165)

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DLMF:7.19.E3
No description defined

    Statements

    DLMF defining formula
    𝖴 ⁡ ( x , t ) + i ⁢ 𝖵 ⁡ ( x , t ) = π 4 ⁢ t ⁢ e z 2 ⁢ erfc ⁡ z , Voigt-U 𝑥 𝑡 𝑖 Voigt-V 𝑥 𝑡 𝜋 4 𝑡 superscript 𝑒 superscript 𝑧 2 complementary-error-function 𝑧 {\displaystyle{\displaystyle\mathsf{U}\left(x,t\right)+i\mathsf{V}\left(x,t% \right)=\sqrt{\frac{\pi}{4t}}e^{z^{2}}\operatorname{erfc}z,}}
    0 references
    constraint
    z = ( 1 - i ⁢ x ) / ( 2 ⁢ t ) 𝑧 1 𝑖 𝑥 2 𝑡 {\displaystyle{\displaystyle z=(1-ix)/(2\sqrt{t})}}
    0 references
    Symbols used
    Voigt function
    DLMF defining formula
    𝖴 ⁡ ( x , t ) Voigt-U 𝑥 𝑡 {\displaystyle{\displaystyle\mathsf{U}\left(\NVar{x},\NVar{t}\right)}}
    xml-id
    C7.S19.E1.m2aadec
    0 references
    Voigt function
    DLMF defining formula
    𝖵 ⁡ ( x , t ) Voigt-V 𝑥 𝑡 {\displaystyle{\displaystyle\mathsf{V}\left(\NVar{x},\NVar{t}\right)}}
    xml-id
    C7.S19.E2.m2aadec
    0 references
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
    complementary error function
    DLMF defining formula
    erfc ⁡ z complementary-error-function 𝑧 {\displaystyle{\displaystyle\operatorname{erfc}\NVar{z}}}
    xml-id
    C7.S2.E2.m2adec
    0 references
    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
    0 references
    imaginary unit
    DLMF defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    real variable
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C7.S1.XMD1.m1bdec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C7.S1.XMD2.m1dec
    0 references

    Identifiers

     
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