Formula:3069

Digital Library of Mathematical Functions ID 7.7.E1

${\displaystyle{\displaystyle\operatorname{erfc}z=\frac{2}{\pi}e^{-z^{2}}\int_{0}^{\infty}\frac{e^{-z^{2}t^{2}}}{t^{2}+1}\mathrm{d}t,}}$

Constraint(s)

${\displaystyle{\displaystyle|\operatorname{ph}z|\leq\frac{1}{4}\pi}}$

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
• ${\displaystyle{\displaystyle\operatorname{ph}}}$: phase
• ${\displaystyle{\displaystyle z}}$: complex variable
 

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