The solutions of the Boole differential equation are ratios of Bessel functions. In many cases these simplify to monomials, modular forms, variations of trigonometric functions, and logarithms. The number of terms used in the continued fraction expansion is
,
is the domain on the
axis ("x range"), and
is the range of values displayed on the
axis ("y range").
Snapshot 1: gamma = 0, --> monomials (
is the exponent). No residual error.
Snapshot 2: alpha = 0, --> modular forms (
is the exponent of the
term under the square root). There are always two solutions.
Snapshot 3: Bessel functions simplify to exponential functions.
