Calculating Elliptic Integrals - Ask Experts for Help

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Discussion Overview

The discussion centers around the calculation of elliptic integrals, particularly in the context of magnetic fields in coils. Participants seek resources for both theoretical understanding and practical exercises related to elliptic integrals.

Discussion Character

  • Homework-related, Technical explanation, Exploratory

Main Points Raised

  • Aldo requests recommendations for textbooks or online resources to learn about elliptic integrals and their calculations.
  • One participant notes that elliptic integrals generally cannot be calculated analytically and typically require numerical methods, mentioning historical resources that compile values of elliptic integrals.
  • Aldo acknowledges the need for numerical methods and specifies the application of elliptic integrals to magnetic fields in coils.
  • Another participant suggests that for extremely thin coils, analytic formulas from a 1963 publication can be used, while also offering their own developed formulas and computer codes for more general cases.

Areas of Agreement / Disagreement

Participants generally agree that elliptic integrals cannot be calculated analytically and require numerical methods. However, there are differing views on the applicability of specific formulas based on the thickness of the coils.

Contextual Notes

The discussion does not resolve the specific conditions under which different methods may be applied, nor does it clarify the limitations of the suggested resources.

Who May Find This Useful

Readers interested in elliptic integrals, numerical methods in physics, and applications in magnetic field calculations may find this discussion relevant.

cataldo
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Hi everybody.
I have a simple question for experts of the forum. I must calculate a elliptic integral.. I do not found on my texbooks how calculate it..
Can suggest me some texbooks or internet sites where i must see their calculate?...I have need to have informations on theory and exercise...
Best regards
Aldo
 
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Elliptic integrals in general can't be calculated analytically, by finding an anti-derivative, and require a numerical integration, say by Simpson's rule.

When I was in college, I remember seeing a bookcase in the college library holding forty volumes of nothing but values of Elliptic integrals for various values of the parameters!
 
Hi hallsofIvy...
Tanks for your replay...
I know that elliptic integrals can be calculated with numerical methods and never analytically... but i have need some titles of the textbooks on elliptic intgrals...I must calculated an elliptic integral on magnetic field in coil for magetic particle testing...
 
If your coils are extremely thin, you can use the analytic formulas published by Milan Wayne Garrett in 1963 in the Journal of Applied Physics. (These formulas use Elliptic Integrals of all three kinds. You can evaluate these elliptic integrals using Carlson's algorithms.) If your coils are *not* extremely thin, I have developed formulas and computer codes that are accurate to one part ber billion, or better, even inside the coils.
 
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