= Weierstrass sigma function
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{title2=$\sigma_\Lambda(z)=z\prod_{\omega\in\Lambda\setminus\{0\}}(1-z/\omega)e^{z/\omega+z^2/(2\omega^2)}$}
For a <period lattice>, the displayed canonical product converges normally because its logarithmic tails are bounded by a constant times $|\omega|^{-3}$. It defines an odd entire function with simple zeros exactly at the lattice and derivative one at zero. Its logarithmic derivative is the <Weierstrass zeta function>, and the derivative of that logarithmic derivative is minus the <Weierstrass elliptic function>. Sigma is quasi-periodic rather than elliptic; balanced products of its translates construct meromorphic functions with prescribed <divisors> on a complex torus.
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