Integral representation of Weil's elliptic functions
Su Hu, Min-Soo Kim
TL;DR
This paper introduces a two-dimensional Euler-MacLaurin formula and uses it to derive an integral representation of Weil's elliptic functions, enhancing understanding of their structure and properties.
Contribution
It presents a novel two-dimensional Euler-MacLaurin summation formula and applies it to obtain an integral representation of Weil's elliptic functions, expanding analytical tools for elliptic functions.
Findings
Derived a two-dimensional Euler-MacLaurin summation formula
Obtained an integral representation of Weil's elliptic functions
Enhanced analytical understanding of elliptic functions
Abstract
In this paper, we give a two dimensional analogue of the Euler-MacLaurin summation formula. By using this formula, we obtain an integral representation of Weil's elliptic functions which was introduced in the book "Elliptic functions according to Eisenstein and Kronecker".
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Taxonomy
TopicsAdvanced Mathematical Identities · Analytic Number Theory Research · Mathematical functions and polynomials