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abdo375
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Can anyone compute the integration of the error function?
Sure. There are tables for this,too. Look in Abramowitz & Stegun for the treatment of "erf". And i'd try lokking in Gradsteyn & Rytzik, too.
Daniel.
FWIW - the standard C library (C99) supports erf() the error function and
erfc() the complement of the error function.
See this page for a numeric method (in the comments section of the code for erf.c)
http://www.ks.uiuc.edu/Research/namd...8C-source.html
Then what DO you mean? The only way to get values for erf(x) itself is to use numerical methods- that isn't going to be any "analytic" way to get a closed form for its integral.abdo375 said:No i meant the actual derivation of the results in the tables...
Isn't there any other way except the numerical method ?
I said this in another threadabdo375 said:See the problem is that I was trying to find the steps that lead this integration [tex] \int^{\infty}_{0}e^{-u^{2}}du [/tex] to equal the square root of pi so I did some research and found that if the integration was computed without it's limits it will give the square root of pi multiplied by the error function so now I'm trying to find the value of the error function with it's limits from zero to infinity.
or can someone tell me if all i did was wrong and there is a whole other way to computing this integral.
another threadlurflurf said:This page about statistics
http://www.york.ac.uk/depts/maths/histstat/
has an article called Information on the History of the Normal Law
in which the desired integral is found 7 ways.
The error function, denoted as erf(x), is a mathematical function used to measure the deviation between an observed value and the true value. It is commonly used in probability and statistics to calculate the area under a normal distribution curve. In integration calculations, it helps to determine the probability that a random variable falls within a certain range of values.
The integration of error function can be calculated using various numerical methods, such as Simpson's rule or Gaussian quadrature. It involves breaking down the area under the curve into smaller segments and approximating the value within each segment using a polynomial function. The sum of these approximations gives an estimate of the integral value.
The integration of error function has various applications in fields such as physics, engineering, and finance. It is commonly used to analyze data and make predictions based on probability distributions. In physics, it is used to calculate the probability of a particle being in a particular energy state. In finance, it is used to calculate the risk of a portfolio's return falling within a certain range.
The complementary error function, denoted as erfc(x), is the complement of the error function, i.e., 1-erf(x). They are closely related and are used interchangeably in many mathematical calculations. The erfc(x) is commonly used in integration calculations as it has a simpler form compared to the erf(x).
To calculate the integration of error function for a specific range of values, we need to first determine the limits of integration. This can be done by using the properties of the error function, such as symmetry and the relationship between erf(x) and erfc(x). Once the limits are determined, we can then use numerical methods to approximate the integral value. Alternatively, it can be calculated using specialized software or calculators.