Abstract
A hyperelliptic integral is by definition an integral of the form
where γ is a path in the complex plane ℂ with coordinate z and f(z) = (z - a 1) ... (z - a d ) with pairwise different constants a i If d = deg f is 1 or 2, an explicit integration by elementary functions is well known from calculus. If d = 3 or 4, integration is possible using elliptic functions. If however d ≥ 5, no explicit integration is known in general.
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© 1992 Springer-Verlag Berlin Heidelberg
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Lange, H., Birkenhake, C. (1992). Introduction. In: Complex Abelian Varieties. Grundlehren der mathematischen Wissenschaften, vol 302. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02788-2_1
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DOI: https://doi.org/10.1007/978-3-662-02788-2_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-02790-5
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