Several transformations have been suggested for proportions x. Most of these require that 0 < x < 1 and therefore fail when x = 0 or x = 1, which is quite common in practice. The paper proposes a ...

As in [Entire slice regular functions, Springer, 2016] we define the ∗-exponential of a slice-regular function, which can be seen as a generalization of the complex exponential to quaternions.