Regular Singular Point

Consider a second-order ordinary differential equation


If P(x) and Q(x) remain finite at x=x_0, then x_0 is called an ordinary point. If either P(x) or Q(x) diverges as x->x_0, then x_0 is called a singular point. If either P(x) or Q(x) diverges as x->x_0 but (x-x_0)P(x) and (x-x_0)^2Q(x) remain finite as x->x_0, then x=x_0 is called a regular singular point (or nonessential singularity).

See also

Irregular Singularity, Singular Point

Explore with Wolfram|Alpha


Arfken, G. "Singular Points." §8.4 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 451-453 and 461-463, 1985.

Referenced on Wolfram|Alpha

Regular Singular Point

Cite this as:

Weisstein, Eric W. "Regular Singular Point." From MathWorld--A Wolfram Web Resource.

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