Formula:3165

Digital Library of Mathematical Functions ID 7.19.E3

${\displaystyle{\displaystyle\mathsf{U}\left(x,t\right)+i\mathsf{V}\left(x,t\right)=\sqrt{\frac{\pi}{4t}}e^{z^{2}}\operatorname{erfc}z,}}$

Constraint(s)

${\displaystyle{\displaystyle z=(1-ix)/(2\sqrt{t})}}$

Symbols List

• ${\displaystyle{\displaystyle\mathsf{U}\left(\NVar{x},\NVar{t}\right)}}$: Voigt function
• ${\displaystyle{\displaystyle\mathsf{V}\left(\NVar{x},\NVar{t}\right)}}$: Voigt function
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\operatorname{erfc}\NVar{z}}}$: complementary error function
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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