The complementary error function is defined as
A) $\operatorname { erfc } ( x ) = \int _ { 0 } ^ { x } e ^ { - u ^ { 2 } } d u$
B) $\operatorname { erfc } ( x ) = \int _ { 0 } ^ { \infty } e ^ { - u ^ { 2 } } d u$
C) $\operatorname { erfc } ( x ) = 2 \int _ { 0 } ^ { x } e ^ { - u ^ { 2 } } d u / \pi$
D) $\operatorname { erfc } ( x ) = 2 \int _ { x } ^ { \infty } e ^ { - u ^ { 2 } } d u / \sqrt { \pi }$
E) $\operatorname { erfc } ( x ) = 2 \int _ { 0 } ^ { x } e ^ { - u ^ { 2 } } d u / \sqrt { \pi }$

Question

Quizplus · Accepted Answer

The complementary error function, $\operatorname{erfc}(x)$, is defined as $1 - \operatorname{erf}(x)$, where $\operatorname{erf}(x)$ is the error function. The correct definition involves an integral from $x$ to $\infty$ of $e^{-u^2}$ scaled by $\frac{2}{\sqrt{\pi}}$, which matches option D.

The Complementary Error Function Is Defined as A) erfc⁡(x)=∫0xe−u2du\operatorname { erfc } ( x ) = \int _ { 0 } ^ { x } e ^ { - u ^ { 2 } } d uerfc(x)=∫0x​e−u2du

The Complementary Error Function Is Defined as
A) $\operatorname { erfc } ( x ) = \int _ { 0 } ^ { x } e ^ { - u ^ { 2 } } d u$