Formula:3071

Digital Library of Mathematical Functions ID 7.7.E3

${\displaystyle{\displaystyle\int_{0}^{\infty}e^{-at^{2}+2izt}\mathrm{d}t=\frac{1}{2}\sqrt{\frac{\pi}{a}}e^{-z^{2}/a}+\frac{i}{\sqrt{a}}F\left(\frac{z}{\sqrt{a}}\right),}}$

Constraint(s)

${\displaystyle{\displaystyle\Re a>0}}$

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
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\Re}}$: real part
• ${\displaystyle{\displaystyle z}}$: complex variable
 

Resources that cite this formula

No records found.