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Complete Elliptic Integral

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Hi everyone!

 

It seems strange to me, but I am not finding in the forum any previous post to the subject.  I need to calculate the Complete Elliptic Integral of the 2nd kind.

 

Since it will be evaluated many times inside a double loop, it would be probably unwise to define it using its "integral definition", because of performance.

 

(from Wikipedia... sorry, I am not a mathematician...)

 

Unbenannt.JPG

 

Has someone good advice for me?  What I am going to try is to use the "Gauss hypergeometric function" that seems to be available in Mathcad (fhyper)

 

Nevertheless I am unsure if this is a good idea.

 

Thanks a lot for any hints

 

Best regards

Claudio


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