In 1-D, the Gaussian function is the function from the Gaussian Distribution,

(1) |

(2) |

(3) |

(4) |

(5) |

(6) |

(7) |

(8) |

In 2-D, the circular Gaussian function is the distribution function for uncorrelated variables and having a
Gaussian Bivariate Distribution and equal Standard Deviation
,

(9) |

(10) |

The above plots show the real and imaginary parts of together with the complex absolute value .

The Gaussian function can also be used as an Apodization Function, shown above with the corresponding Instrument Function.

The Hypergeometric Function is also sometimes known as the Gaussian function.

**References**

MacTutor History of Mathematics Archive. ``Frequency Curve.'' http://www-groups.dcs.st-and.ac.uk/~history/Curves/Frequency.html.

© 1996-9

1999-05-25