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Gaussian integral ( $\int_{- \infty}^{\infty} e^{- x^{2}} d x = π$ )

The Gaussian integral is

\int_{- \infty}^{\infty} e^{- a x^{2}} d x = \frac{π}{a}, a > 0.

Squaring the integral and changing to polar coordinates proves the formula.

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- Error function Gaussian integral 15

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