Proofs of fast formulas for computing constant pi

AI Thread Summary
The discussion focuses on the mathematical background and proofs of fast algorithms for computing the constant pi, specifically mentioning the Gauss-Legendre algorithm, Borwein algorithm, Ramanujan formulas, and Chudnovsky formula. There is a request for online resources and textbooks that provide complete proofs for these algorithms. The user has demonstrated proficiency in general mathematics and has proven a relation involving the arithmetic-geometric mean and elliptic integrals. However, they are seeking further guidance and resources on this topic. The conversation highlights a need for shared knowledge and references in the mathematical community regarding these algorithms.
Nedeljko
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I am interesting for mathematical background od fast algorithms for computing number \pi with complete proofs only. More specific, I am interesting for Gauss Legendre algorithm, Borwein algorithm, Ramanujan formulas and Chudnovsky formula.
 
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Is there any online source about this topic?

I am skillful in general mathematics. About Gauss Legendre formula, how to prove relation between arithmetic-geometric mean and complete elliptic integral of the first kind? I proved that it is equivalent to formula K(\sin^2(2x))\cos^2x=K(\tan^4x), where K is the complete elliptic integral of the first kind.
 
Nedeljko said:
Is there any online source about this topic?
I've searched a bit online, but haven't, as yet, dug up any. Hopefully, somebody else might lead you there. :smile:
 
Does somebody has ideas for proofs or links?
 

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