Mathieu Equation
The canonical form for Mathieu's differential equation is
The Mathieu equation is a Hill equation with only 1 harmonic mode. Closely related is Mathieu's modified differential equation
which follows on substitution .
The substitution transforms Mathieu's equation to the algebraic form
This has two regular singularities at and one irregular singularity at infinity, which implies that in general (unlike many other special functions), the solutions of Mathieu's equation cannot be expressed in terms of hypergeometric functions.
Mathieu's differential equations arise as models in many contexts, including the stability of railroad rails as trains drive over them, seasonally forced population dynamics, the four-dimensional wave equation, and the Floquet theory of the stability of limit cycles.
Read more about this topic: Mathieu Function
Famous quotes containing the word equation:
“Jail sentences have many functions, but one is surely to send a message about what our society abhors and what it values. This week, the equation was twofold: female infidelity twice as bad as male abuse, the life of a woman half as valuable as that of a man. The killing of the woman taken in adultery has a long history and survives today in many cultures. One of those is our own.”
—Anna Quindlen (b. 1952)