Article
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Addition Formula of the Theta Function and Square Sums Theorem
Version 1
: Received: 3 July 2023 / Approved: 5 July 2023 / Online: 6 July 2023 (08:50:25 CEST)
How to cite: Zhai, H.C. Addition Formula of the Theta Function and Square Sums Theorem. Preprints 2023, 2023070401. https://doi.org/10.20944/preprints202307.0401.v1 Zhai, H.C. Addition Formula of the Theta Function and Square Sums Theorem. Preprints 2023, 2023070401. https://doi.org/10.20944/preprints202307.0401.v1
Abstract
Jacobian theta function identities are related to the Addition formula for the Weierstrass 1 Sigma function. In this paper, from the Addition formula for Weierstrass Sigma function, new and 2 simple proofs of four square sums theorem are given. Using the addition formula of the theta func- 3 tions, we also give simple proofs of two square sums and eight square sums theorem.
Keywords
Theta function; Weierstrass Sigma function; Weierstrass Elliptic function; Square sums 5 theorem
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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