Formula:3074

Digital Library of Mathematical Functions ID 7.7.E6

${\displaystyle{\displaystyle\int_{x}^{\infty}e^{-(at^{2}+2bt+c)}\mathrm{d}t=\frac{1}{2}\sqrt{\frac{\pi}{a}}e^{(b^{2}-ac)/a}\operatorname{erfc}\left(\sqrt{a}x+\frac{b}{\sqrt{a}}\right),}}$

Constraint(s)

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

Symbols List

• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\operatorname{erfc}\NVar{z}}}$: complementary error function
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\Re}}$: real part
• ${\displaystyle{\displaystyle x}}$: real variable
 

Resources that cite this formula

No records found.