Finite and infinite product transformations

2017/12/17 by Martin Nicholson, Nicholson, Martin
Computer Science · Mathematics · #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematics and Applications #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1712.06097

openalex publication_date 2017/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Several infinite products are studied that satisfy the transformation relation of the type f(α)=f(1/α). For certain values of the parameters these infinite products reduce to modular forms. Finite counterparts of these infinite products are motivated by solution of Dirichlet boundary problem on a rectangular grid. These finite product formulas give an elementary proof of several modular transformations.

Related

• Elliptic functions, infinite products and modular relations
• Novel Approach to Infinite Products Using Multiplicative Modulus\n Function
• Infinite products in number theory and geometry
• A modular type formula for Euler infinite product (1-x)(1-xq)(1-xq²)(1-xq³)...
• On the Modular Behaviour of the Infinite Product (1-x)(1-xq)(1-xq²)(1-xq³)...