Proofs of fast formulas for computing constant pi

[Nedeljko]

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.

 

[arildno]

Have you considered buying a text-book?

 

[Nedeljko]

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.

 

[arildno]

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.

 

[Nedeljko]

Does somebody has ideas for proofs or links?