Irregular Singularity

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. 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. 451-453 and 461-463, 1985.