New representations of Taylor coefficients of the Weierstrass sigma-function

Details New representations of Taylor coefficients of the Weierstrass sigma-function New representations of Taylor coefficients of the Weierstrass sigma-function

2009-09-19

arxiv.org/abs/0909.3597v1

Mathematics

Complex Variables

17 pages

Scientific paper

We provide two kinds of representations for the Taylor coefficients of the Weierstrass sigma-function associated to an arbitrary lattice in the complex plane $\mathbb{C}$. The first one in terms of Hermite-Gauss series over such lattice and the second one in terms of Hermite-Gauss integrals over $\mathbb{C}$. As applications, we derive identities of arithmetic type relating some modular forms to such Hermite-Gaussian series. This will be possible by comparing our obtained representations to the one elaborated by Weierstrass himself in 1882.

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