What does |x| mean in the erf function?

moonman239 · 2010-09-11T22:03:22+00:00

Here's the equation I'm using: erf(x) = x/|x| * SQRT(1 - exp(-x2*(4/pi + (ax)2) / (1 + ax2)

Thread starter moonman239
Start date Sep 11, 2010
Tags

Function Mean

In summary, the erf function is a mathematical function used to calculate the area under a Gaussian curve. It is closely related to the normal distribution and is commonly used in probability and statistics. The |x| in the erf function represents the absolute value of the input value, used to calculate the probability of a certain value occurring within a given range. The function has various applications in mathematics, statistics, and engineering, and is typically calculated using numerical methods such as infinite series approximation or special functions.

Sep 11, 2010

moonman239

Here's the equation I'm using: erf(x) = x/|x| * SQRT(1 - exp(-x²*(4/pi + (ax)²) / (1 + ax²)

Physics news on Phys.org

Sep 11, 2010

awkward

moonman239 said:

Here's the equation I'm using: erf(x) = x/|x| * SQRT(1 - exp(-x²*(4/pi + (ax)²) / (1 + ax²)

|x| is the absolute value of x.

x/|x| is 1 for positive x, -1 for negative x.

(However, I don't recognize that equation for erf.)

FAQ: What does |x| mean in the erf function?

What is the erf function?

The erf function, also known as the error function, is a mathematical function used to calculate the area under a Gaussian curve. It is commonly used in statistics and probability theory.

What does the |x| mean in the erf function?

The |x| in the erf function represents the absolute value of the input value, which is the distance from the mean in a normal distribution. It is used to calculate the probability of a certain value occurring within a given range.

How is the erf function related to the normal distribution?

The erf function is closely related to the normal distribution as it is used to calculate the probability of a value occurring within a certain range in a normal distribution. The erf function is also known as the cumulative distribution function (CDF) of the standard normal distribution.

What are the applications of the erf function?

The erf function has various applications in mathematics, statistics, and engineering. It is commonly used in probability and statistics to calculate the area under the Gaussian curve. It is also used in signal processing, quantum mechanics, and other fields.

How is the erf function calculated?

The erf function is typically calculated using numerical methods as it does not have a closed-form solution. One common method is to use an infinite series approximation, such as the Taylor series. Other methods include using special functions or software packages that have built-in functions for calculating the erf function.