Calculating the Integration of Error Function

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Discussion Overview

The discussion revolves around the integration of the error function, specifically seeking methods for deriving results related to the integral of the error function and its connection to the Gaussian integral.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants suggest consulting tables such as those in Abramowitz & Stegun and Gradsteyn & Rytzik for values of the error function.
  • One participant mentions that the standard C library includes functions for the error function and its complement, indicating a numeric method for computation.
  • There is a request for a derivation of the integral of the error function rather than just numerical methods, with a participant asserting that no analytic closed form exists for its integral.
  • A participant expresses confusion regarding the steps leading to the integral of \( \int^{\infty}_{0}e^{-u^{2}}du \) equating to the square root of pi, and seeks clarification on whether their understanding is correct.
  • Another participant references a historical article discussing multiple methods for computing the integral in question.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the methods for integrating the error function, with some advocating for numerical methods while others seek analytic approaches. The discussion remains unresolved regarding the derivation of the integral.

Contextual Notes

There are unresolved assumptions regarding the methods of integration and the definitions of the error function, as well as the limitations of numerical versus analytic approaches.

abdo375
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Can anyone compute the integration of the error function?
 
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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.
 
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.

No i meant the actual derivation of the results in the tables...



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


Isn't there any other way except the numerical method ?
 
Last edited by a moderator:
abdo375 said:
No i meant the actual derivation of the results in the tables...
Isn't there any other way except the numerical method ?
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.
 
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.
 
Last edited:
abdo375 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.
I said this in another thread
lurflurf 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.
another thread
https://www.physicsforums.com/showthread.php?t=81662
 
Last edited:
Yeah that's just all i need
thank you all for your contributions.
 

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