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arXiv · 1906.02141

Meromorphic functions in a first-order system

P. L. Robinson
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Abstract

We consider the differential equations $s' = c^5$ and $c' = - s^5$ with initial conditions $s(0) = 0$ and $c(0) = 1$. We show that $s^2 c^2$ extends to the reciprocal of the Weierstrass elliptic function with invariants $g_2 = 0$ and $g_3 = 16$. We also show that powers of $s^2 c^2$ are the only functions of the form $s^m c^n$ that extend meromorphically in the plane.

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P. L. Robinson. 2019-06-02. Meromorphic functions in a first-order system. https://arxiv.org/abs/1906.02141

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