Regular Singular Point
In mathematics, in the theory of ordinary differential equations in the complex plane, the points of are classified into ordinary points, at which the equation's coefficients are analytic functions, and singular points, at which some coefficient has a singularity. Then amongst singular points, an important distinction is made between a regular singular point, where the growth of solutions is bounded (in any small sector) by an algebraic function, and an irregular singular point, where the full solution set requires functions with higher growth rates. This distinction occurs, for example, between the hypergeometric equation, with three regular singular points, and the Bessel equation which is in a sense a limiting case, but where the analytic properties are substantially different.
Read more about Regular Singular Point: Formal Definitions, Examples For Second Order Differential Equations, Hermite Differential Equation
Famous quotes containing the words regular, singular and/or point:
“The solid and well-defined fir-tops, like sharp and regular spearheads, black against the sky, gave a peculiar, dark, and sombre look to the forest.”
—Henry David Thoreau (1817–1862)
“Not from this anger, anticlimax after
Refusal struck her loin and the lame flower
Bent like a beast to lap the singular floods....”
—Dylan Thomas (1914–1953)
“Lieutenant, I’d like to point out to you that I don’t have to put up with this crap from you. I’m not in your two-bit army, I’m in our two-bit army.”
—Bryan Forbes (b. 1926)