abelian function

An abelian or hyperelliptic function is a generalisation of an elliptic function. It is a function of two variables with four periods.In a similar way to an elliptic function it can also be regarded as the inverse function to certain integrals (called abelian or hyperelliptic integrals) of the form

$$\int \frac{dz}{R(z)}$$

where $R$ is a polynomial of degree greater than 4.