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Integrating the Gaussian. For each real x we let
 

Summary: Integrating the Gaussian.
For each real x we let
(x) =
1

2
e- x2
2
and we let
(x) =
x
-infty
(w) dw.
is called the standard Gaussian (I think) and is called the standard error function.
Theorem. We have

-
(x) dx = 1.
One of many proofs. We have

  

Source: Allard, William K. - Department of Mathematics, Duke University

 

Collections: Mathematics