Calculating Elliptic Integrals - Ask Experts for Help

[cataldo]

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

 

[HallsofIvy]

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!

 

[cataldo]

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...

 

[Carl_Weggel]

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.