English

Finite and infinite product transformations

Classical Analysis and ODEs 2020-01-03 v2

Abstract

Several infinite products are studied that satisfy the transformation relation of the type f(α)=f(1/α)f(\alpha)=f(1/\alpha). 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.

Keywords

Cite

@article{arxiv.1712.06097,
  title  = {Finite and infinite product transformations},
  author = {Martin Nicholson},
  journal= {arXiv preprint arXiv:1712.06097},
  year   = {2020}
}

Comments

12 pages. Presentation and notation improved, 6 new theorems added, typos corrected, more details added in abstract

R2 v1 2026-06-22T23:20:34.683Z