Formula:3045

Digital Library of Mathematical Functions ID 7.5.E1

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \DawsonsintF@{z}=\tfrac{1}{2}i\sqrt{\pi}\left(e^{-z^{2}}-\Faddeevaw@{z}\right)=-\tfrac{1}{2}i\sqrt{\pi}e^{-z^{2}}\erf@{iz}.}

Symbols List

• ${\displaystyle{\displaystyle F\left(\NVar{z}\right)}}$: Dawson’s integral
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\operatorname{erf}\NVar{z}}}$: error function
• ${\displaystyle{\displaystyle w\left(\NVar{z}\right)}}$: Faddeeva (or Faddeyeva) function
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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