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:
“A regular council was held with the Indians, who had come in on their ponies, and speeches were made on both sides through an interpreter, quite in the described mode,—the Indians, as usual, having the advantage in point of truth and earnestness, and therefore of eloquence. The most prominent chief was named Little Crow. They were quite dissatisfied with the white man’s treatment of them, and probably have reason to be so.”
—Henry David Thoreau (1817–1862)
“English general and singular terms, identity, quantification, and the whole bag of ontological tricks may be correlated with elements of the native language in any of various mutually incompatible ways, each compatible with all possible linguistic data, and none preferable to another save as favored by a rationalization of the native language that is simple and natural to us.”
—Willard Van Orman Quine (b. 1908)
“Consider a man riding a bicycle. Whoever he is, we can say three things about him. We know he got on the bicycle and started to move. We know that at some point he will stop and get off. Most important of all, we know that if at any point between the beginning and the end of his journey he stops moving and does not get off the bicycle he will fall off it. That is a metaphor for the journey through life of any living thing, and I think of any society of living things.”
—William Golding (b. 1911)