Infinite Products

Abstract

We consider an infinite product of quaternions

$$q_{0}\ q_{1}\ldots q_{i}\ldots = \prod_{i=0}^{\infty }q_{ i}$$

and, for $n \in \mathbb{N}$, we denote by $Q_{n} = q_{0}q_{1}\ldots q_{n}$ the partial products. In analogy with the complex case (see [4]), we give the following definition.