Extended Landen's formulas and double product theta functions

2024/12/08 by Kiyoshi Sogo, Sogo, Kiyoshi
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Mathematical Inequalities and Applications

paper · pdf · doi:10.48550/arxiv.2412.06081

Abstract

For an arbitrary positive integer p, Landen's formula is extended to express theta function with modulus pτ by p product of theta functions with τ, which is applied to several examples. Next it is shown that double product of theta functions of genus g=1 is written by a sum of g=2 theta functions, which is a subset having a special period matrix of τ₁₁=τ₂₂. Several applied examples are shown, which include the cubic identity of Borwein and Borwein.

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