DLMF:7.19.E3 (Q2467)

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DLMF:7.19.E3
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    Statements

    test
    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
    DLMF id
    DLMF:7.19.E3
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    constraint
    z = ( 1 - i ⁢ x ) / ( 2 ⁢ t ) 𝑧 1 𝑖 𝑥 2 𝑡 {\displaystyle{\displaystyle z=(1-ix)/(2\sqrt{t})}}
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    Symbols used
    Voigt function
    test
    𝖴 ⁡ ( x , t ) Voigt-U 𝑥 𝑡 {\displaystyle{\displaystyle\mathsf{U}\left(\NVar{x},\NVar{t}\right)}}
    xml-id
    C7.S19.E1.m2aadec
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    Voigt function
    test
    𝖵 ⁡ ( x , t ) Voigt-V 𝑥 𝑡 {\displaystyle{\displaystyle\mathsf{V}\left(\NVar{x},\NVar{t}\right)}}
    xml-id
    C7.S19.E2.m2aadec
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    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
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    complementary error function
    test
    erfc ⁡ z complementary-error-function 𝑧 {\displaystyle{\displaystyle\operatorname{erfc}\NVar{z}}}
    xml-id
    C7.S2.E2.m2adec
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    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
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    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
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