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There are many elliptic integrals, so to show my point let me just pick one of them (complete elliptic integral of the first kind [1]): $$K(k) = \int_{0}^{1} \frac {dx} {\sqrt{(1-x^{2})(1-k^{2}x^{2})}}...

A great part of complex geometry and, algebraic geometry has been developed to address the theory of abelian integrals/functions. A very special problem that kept many great mathematicians busy was ...