Regular singular point
Regular singularity; Irregular singular point; Irregular singularity; Regular singular points; Linear differential equation of the Fuchsian class; Regular singularities; Nonessential singularity; Regular differential equation; Fuchsian differential equation; Fuchsian equation
In mathematics, in the theory of ordinary differential equations in the complex plane \Complex, the points of \Complex 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.