Degenerate
A limiting case in which a class of object changes its nature so as to belong to another, usually simpler, class. Forexample, the Point is a degenerate case of the Circle as the Radius approaches 0, and theCircle is a degenerate form of an Ellipse as the Eccentricity approaches 0. Another example is the twoidentical Roots of the second-order Polynomial 
. Since the 
Roots of an th degreePolynomial are usually distinct, Roots which coincide are said to be degenerate. Degenerate cases often requirespecial treatment in numerical and analytical solutions. For example, a simple search for both Roots of the aboveequation would find only a single one: 1.
The word degenerate also has several very specific and technical meanings in different branches of mathematics.
References
Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 513-514, 1985.
- Points Problem
- Pointwise Dimension
- Poisson Bracket
- Poisson-Charlier Function
- Poisson-Charlier Polynomial
- Poisson Distribution
- Poisson Integral
- Poisson Integral Representation
- Poisson Kernel
- Poisson Manifold
- Poisson's Bessel Function Formula
- Poisson's Equation
- Poisson's Harmonic Function Formula
- Poisson Sum Formula
- Poisson Trials
- Poke Move
- Poker
- Polar
- Polar Angle
- Polar Circle
- Polar Coordinates
- Polarity
- Polar Line
- Pole
- Pole (Geometry)