WOLFRAM|DEMONSTRATIONS PROJECT

Boole Differential Equation with Continued Fractions

​
n
γ
β
α
δ
k
xr
yr
Boole's Equation
γ
2
y(x)
+βy(x)+xα
′
y
(x)δ
k
x
-3x
′
y
(x)+3
2
y(x)
+4y(x)-2
5
x
-
2
3
5/2
x
J
-
11
15
2
5
2
3
5/2
x
J
4
15
2
5
2
3
5/2
x
-
4
3
-
2
5
x
-19-
6
5
x
-34-
6
5
x
-49-
6
5
x
-64-
6
5
x
-79-
6
5
x
-94+
6
5
x
109
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.