Abelian integral

In mathematics, an abelian integral, named after the Norwegian mathematician Niels Abel, is an integral in the complex plane of the form

where ${\displaystyle R(x,w)}$ is an arbitrary rational function of the two variables ${\displaystyle x}$ and ${\displaystyle w}$, which are related by the equation

where ${\displaystyle F(x,w)}$ is an irreducible polynomial in ${\displaystyle w}$,

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