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

Question

Quizplus · Accepted Answer

The error function, denoted as $\operatorname{erf}(x)$, is correctly defined by choice E, which includes the factor of $2/\sqrt{\pi}$ to normalize the integral over the entire real line.

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

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