ARTICLE | doi:10.20944/preprints202307.0401.v1
Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Theta function; Weierstrass Sigma function; Weierstrass Elliptic function; Square sums 5 theorem
Online: 6 July 2023 (08:50:25 CEST)
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.
ARTICLE | doi:10.20944/preprints202307.0252.v1
Subject: Computer Science And Mathematics, Algebra And Number Theory Keywords: Ramanujan's theta function; Modular equation; $q$-Shifted factorial
Online: 5 July 2023 (03:39:26 CEST)
We establish certain modular equations of degree three based on some results of Ramanujan's theta functions.