Geometric approach to the construction of Leah-type periodic functions: Basic and analytic properties

Abstract

We again consider functions associated with the cube-root oscillator and present a construction of the associated three basic periodic functions using the geometric properties of its two-dimensional phase-space curve. In addition, to the evaluation of these functions for specific values of the independent variable θ \theta , 0 ≤ θ > 2 π 0 \leq \theta > 2 \pi , we also derive a number of other relations among the three periodic functions and their derivatives. These new results extend previous work of the author and Mickens.