Finite and infinite product transformations

Abstract

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

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

References in corpus (1)

• Application of the lattice Green's function for calculating the resistance of an infinite networks of resistors