M. M. Alekseev, S. I. Bezrodnykh, “System of Partial Differential Equations and Analytical Representations of the Weierstrass Sigma Function”, Mat. Zametki, 2023, Volume 114, Issue 6,Pages <nobr>1094

System of Partial Differential Equations and Analytical Representations of the Weierstrass Sigma Function

M. M. Alekseev^ab, S. I. Bezrodnykh^a

^a Federal Research Center “Computer Science and Control” of Russian Academy of Sciences, Moscow, 119333, Russia
^b Bauman Moscow State Technical University, Moscow, 105005, Russia

Abstract: We obtain a power series representation of the Weierstrass sigma function arising in the theory of elliptic functions and derive a differential–recurrence equation as well as closed-form expressions for its coefficients. These results are obtained using the Weierstrass system of partial differential equations satisfied by the sigma function.

Keywords: elliptic function, Weierstrass function.

Received: 03.10.2023
Revised: 03.10.2023

Language: English