  The Leah-Hamiltonian, $H(x,y)=y^2/2+3x^{4/3}/4$, is introduced as a
functional equation for $x(t)$ and $y(t)$. By means of a nonlinear
transformation to new independent variables, we show that this functional
equation has a special class of periodic solutions which we designate the Imani
functions. The explicit construction of these functions is done such that they
possess many of the general properties of the standard trigonometric cosine and
sine functions. We conclude by providing a listing of a number of currently
unresolved issues relating to the Imani functions.
