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Matematicheskie Zametki, 2023, Volume 114, Issue 6, paper published in the English version journal (Mi mzm14270)  
System of Partial Differential Equations and Analytical Representations of the Weierstrass Sigma Function

M. M. Alekseevab, S. I. Bezrodnykha

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.
Funding agency
This work was supported by ongoing institutional funding.
Received: 03.10.2023
Revised: 03.10.2023
English version:
Mathematical Notes, 2023, Volume 114, Issue 6, Pages 1094–1102
DOI: https://doi.org/10.1134/S0001434623110421
Bibliographic databases:
Document Type: Article
Language: English
Citation: M. M. Alekseev, S. I. Bezrodnykh, “System of Partial Differential Equations and Analytical Representations of the Weierstrass Sigma Function”, Math. Notes, 114:6 (2023), 1094–1102
Citation in format AMSBIB
\Bibitem{AleBez23}
\by M.~M.~Alekseev, S.~I.~Bezrodnykh
\paper System of Partial Differential Equations and Analytical Representations of the Weierstrass Sigma Function
\jour Math. Notes
\yr 2023
\vol 114
\issue 6
\pages 1094--1102
\mathnet{http://mi.mathnet.ru/mzm14270}
\crossref{https://doi.org/10.1134/S0001434623110421}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85187885069}
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