Series and integral representations of the Taylor coefficients of the Weierstrass sigma-function
We provide two kinds of representations for the Taylor coefficients of the Weierstrass $σ$-function $σ(\cdot;Γ)$ associated to an arbitrary lattice $Γ$ in the complex plane $\mathbb{C}=\mathbb{R}^2$ - the first one in terms of the so-called Hermite-Gauss series over $Γ$ and the second one in terms of Hermite-Gauss integrals over $\mathbb{C}$.
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