Explore the profound connection between Euler's Identity and the Taylor series, two foundational concepts in mathematics. This overview explains how the expansion of exponential functions using the ...

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.