Does anyone know how Madhava discovered the power series for the arctangent? I think the standard way is to note that [itex]1-x^2+x^4-\dotsb[/itex] converges uniformly on [itex](-1,1)[/itex] to [itex]\frac{d}{dt}\tan^{-1}x[/itex], and thus applying the fundamental theorem of calculus we may integrate term-by-term. But how did Madhava do it? I don't know that he had the FTOC or a concept of uniform convergence, or even that he knew how to integrate a polynomial.(adsbygoogle = window.adsbygoogle || []).push({});

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# How did Madhava come up with the Arctan series?

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