Novel Approach to Infinite Products Using Multiplicative Modulus Function

Abstract

The usual nonnegative modulus function is based on addition. A natural different modulus function on the set of positive reals is introduced. Arguments for results for series through the usual modulus function are transformed to arguments for results for infinite products through the new modular function for multiplication. Counterparts for Riemann rearrangement theorem and some tests for convergence are derived. These counterparts are completely new results and they are different from classical results for infinite products.