Probability Integral

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$\displaystyle \alpha(x)$	$\textstyle \equiv$	$\displaystyle {1\over\sqrt{2\pi}} \int^x_{-x} e^{-t^2/2}\,dt$	(1)
	$\textstyle =$	$\displaystyle \sqrt{2\over\pi} \int_0^x e^{-t^2/2}\,dt$	(2)
	$\textstyle =$	$\displaystyle 2\Phi(x)$	(3)
	$\textstyle =$	$\displaystyle \mathop{\rm erf}\nolimits \left({x\over\sqrt{2}}\right),$	(4)

where $\Phi(x)$ is the Normal Distribution Function and Erf is the error function.