Boole Differential Equation with Continued Fractions

Explore the solutions of the Boole differential equation with continued fractions. Continued fractions provide a very effective function approximation toolset. Usually the continued fraction expansion of a given function approximates the function better than the Taylor series or the Fourier series. The solution(s) of the Boole differential equation are very diverse; they contain polynomials, trigonometric functions, hyperbolas, (nested) square roots, and modular forms.