Singular Point (Differential Equation)

Consider a second-order Ordinary Differential Equation

If and remain Finite at , then is called an Ordinary Point. If either or diverges as , then is called a singular point. Singular points are further classified as follows:
1. If either or diverges as but and remain Finite as , then is called a Regular Singular Point (or Nonessential Singularity).

2. If diverges more quickly than , so approaches Infinity as , or diverges more quickly than so that goes to Infinity as , then is called an Irregular Singularity (or Essential Singularity).

Arfken, G. Singular Points.'' §8.4 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 451-454, 1985.