Definition:Gaussian Integral/One Variable

Definition

The Gaussian Integral (of one variable) is the following improper integral, considered as a real function:

$\phi_1: \R \to \R$:

$\map {\phi_1} x = \ds \int_{\mathop \to -\infty}^x \frac 1 {\sqrt {2 \pi} } \map \exp {-\frac {t^2} 2 } \rd t$

where $\exp$ is the real exponential function.

Sources

• 2001: Michael A. Bean: Probability: The Science of Uncertainty: $\S 6.3$
• 2011: Charles Henry Brase and Corrinne Pellillo Brase: Understandable Statistics (10th ed.): $\S 6.1$