## How did Madhava come up with the Arctan series?

Does anyone know how Madhava discovered the power series for the arctangent? I think the standard way is to note that $1-x^2+x^4-\dotsb$ converges uniformly on $(-1,1)$ to $\frac{d}{dt}\tan^{-1}x$, 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.
 Recognitions: Homework Help Science Advisor obviously it was revealed by vishnu.

 Quote by mathwonk obviously it was revealed by vishnu.

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