“elliptic function”的概念、定义、习题解题方法及翻译-数学辞典

单词

elliptic function

释义

elliptic function

A meromorphic doubly-periodic function defined on the complex plane such that f(z+ma+nb) = f(z) for all integers m, n, where a/b is not real. Note that such an elliptic function defines a meromorphic function on the elliptic curve ℂ/Λ, where Λ denotes the lattice aℤ + bℤ.

Note further by Liouville's theorem that holomorphic elliptic functions are constant. Elliptic functions became of interest as a consequence of elliptic integrals.

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