What is the equation for error function in heat transfer?

In summary, the error function (erf) is a mathematical function used in heat transfer, statistics, and solving differential equations. It is expressed as (2/sqrt(π)) ∫0..x e-x2 dx and has applications in solving problems involving Gaussian distributions. It is also known as the imaginary error function and has the ability to expand the expressive power of closed forms by representing non-elementary functions. It is often tabulated for easy use in solving differential equations.
  • #1
Saint
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In heat transfer, some formulae are expressed in error function. what is it ?

How do we get the equation for error function ?[?]
 
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  • #2
Isn't the error function e -x 2 ? Thats all I know...
 
Last edited:
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  • #4
Originally posted by On Radioactive Waves
Isn't the error function e -x 2 ? Thats all I know...
I've heard it's called imaginary error function in full.
 
  • #5
Almost... erf(x) is:

erf(x) = (2 / sqrt(π)) ∫0..x e-x2 dx

It's immediate use is that it's the integral of a gaussian distribution, so it's directly applicable to statistical problems.

More generally, I understand that a lot of nonelementary functions can be expressed in terms of combinations of elementary functions and error functions, so erf expands the expressive power of closed forms.
 
  • #6
It comes up when solving some differential equations, and it is thus good to have tabulated.
 

1. What is the error function?

The error function, also known as the Gauss error function, is a mathematical function used to measure the accuracy of a model or approximation in statistics and applied mathematics. It is defined as the integral of a normal distribution with mean 0 and standard deviation of 1.

2. What is the purpose of the error function in statistics?

The error function is commonly used in statistics to evaluate the difference between a predicted value and the actual value of a variable. It is often used in regression analysis to measure the accuracy of a model and to determine the amount of error in the data.

3. How is the error function calculated?

The error function is calculated using an integral, which is a mathematical operation that represents the area under a curve. It is a complex mathematical function that cannot be expressed in terms of elementary functions, but it can be approximated using numerical methods.

4. What are the properties of the error function?

The error function has several important properties, including being an odd function, meaning that f(-x) = -f(x). It also approaches 1 as x approaches infinity and approaches -1 as x approaches negative infinity. Additionally, it is a continuous and differentiable function.

5. What are the applications of the error function?

The error function has various applications in fields such as statistics, physics, engineering, and finance. It is used to calculate probabilities and confidence levels, as well as to evaluate the accuracy of models and approximations. It is also used in the solution of differential equations and in the analysis of signal processing and noise.

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