Series and integral representations of the Taylor coefficients of the Weierstrass sigma-function

Abstract

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

arXiv comment12 pages

References in corpus (1)

• Landau (Γ,χ)-automorphic functions on \mathbb{C}^n of magnitude ν