Formula:3131

Digital Library of Mathematical Functions ID 7.14.E1

${\displaystyle{\displaystyle\int_{0}^{\infty}e^{2iat}\operatorname{erfc}\left(bt\right)\mathrm{d}t={\frac{1}{a\sqrt{\pi}}F\left(\frac{a}{b}\right)+\frac{i}{2a}\left(1-e^{-(a/b)^{2}}\right)},}}$

Constraint(s)

${\displaystyle{\displaystyle a\in\mathbb{C}}}$
${\displaystyle{\displaystyle|\operatorname{ph}b|<\tfrac{1}{4}\pi}}$

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
• ${\displaystyle{\displaystyle\operatorname{erfc}\NVar{z}}}$: complementary error function
• ${\displaystyle{\displaystyle\mathbb{C}}}$:
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\in}}$:
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\operatorname{ph}}}$: phase
 

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