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#### Excited state intramolecular proton transfer in hydroxyanthraquinones: Toward predicting fading of organic red colorants in art - Science Advances

In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the form:

Normalized Gaussian curves with expected value μ and variance σ. The corresponding parameters are ${\displaystyle a={\tfrac {1}{\sigma {\sqrt {2\pi }}}}}$, b = μ, and c = σ.

In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the form:

${\displaystyle f\left(x\right)=ae^{-{\frac {(x-b)^{2}}{2c^{2}}}}}$

for arbitrary real constants a, b and c. It is named after the mathematician Carl Friedrich Gauss.

The graph of a Gaussian is a characteristic symmetric "bell curve" shape. The parameter a is the height of the curve's peak, b is the position of the center of the peak and c (the standard deviation, sometimes called the Gaussian RMS width) controls the width of the "bell".

Gaussian functions are widely used in statistics to describe the normal distributions, in signal processing to define Gaussian filters, in image processing where two-dimensional Gaussians are used for Gaussian blurs, and in mathematics to solve heat equations and diffusion equations and to define the Weierstrass transform.

### The Gaussian Integral

In this video, we try to evaluate the Gaussian integral. Featuring some multi-variable calculus, some graphs and my Paint illustrations. Little background: I first ...

### Gaussian

The most widely used probability distribution function is the Gaussian curve, also known as the normal distribution or the bell curve. In this video I introduce the ...

### How To Integrate The Gaussian Function | HBD Gauss!

Today is Carl Gauss's 241st birthday. What better way to honor him than to integrate the hell out of the function named after him?

### The Gaussian Distribution

Brief introduction to the Gaussian distribution NOTE: This video was originally part of a special series of lectures derived from the material in crp241. There are ...

### Derivation of the Normal (Gaussian) Distribution

In this video, I'll derive the formula for the normal/Gaussian distribution. This argument is adapted from the work of the astronomer John Herschel in 1850 and the ...

### Concept of Gaussian distribution for Dummies

In probability theory, the normal (or Gaussian) distribution is a very commonly occurring continuous probability distribution—a function that tells the probability of ...