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→Formula: Clearer order. |
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\end{align}
</math>
where <math>\Omega</math> is the [[period matrix]] derived from one of the following hyperelliptic integrals
<math display="block">
u(a) = \int^a_1 \frac{dx}{\sqrt{x(x-1)f(x)}}
</math>
Or if <math>f(x)</math> is of
<math display="block">
u(a) = \int^a_1 \frac{dx}{\sqrt{x(x-1) (x-2) f(x)}}
</math>
This formula applies to any algebraic equation of any degree without need for a [[Tschirnhaus transformation]] or any other manipulation to bring the equation into a specific normal form, such as the [[Bring–Jerrard form]] for the quintic. However, application of this formula in practice is difficult because the relevant hyperelliptic integrals and higher genus theta functions are very complex.
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