Regular Singular Point
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 either or diverges as but 
and 
remain Finite as , then is called a regular singular point(or Nonessential Singularity).See also Irregular Singularity, Singular Point (Differential Equation)
References
Arfken, G. ``Singular Points.'' §8.4 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 451-453 and 461-463, 1985.
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