Singular Point (Function)

Singular points (also simply called ``singularities'') are points in the Domain of a Function where fails to be Analytic. Isolated Singularities may beclassified as Essential Singularities, Poles, or RemovableSingularities.

Essential Singularities are Poles of Infinite order.

A Pole of order is a singularity of for which the function is nonsingular and forwhich is singular for , 1, ..., .

Removable Singularities are singularities for which it is possible to assign a ComplexNumber in such a way that becomes Analytic. For example, the function hasa Removable Singularity at 0, since everywhere but 0, and can be set equal to 0 at .Removable Singularities are not Poles.

The function has Poles at , and a nonisolated singularity at 0.

References

Arfken, G. ``Singularities.'' §7.1 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 396-400, 1985.

• Loop (Algebra)
• Loop Gain
• Loop (Graph)
• Loop (Knot)
• Loop Space
• Lorentz Group
• Lorentzian Distribution
• Lorentzian Function
• Lorentz Tensor
• Lorentz Transformation
• Lorenz System
• Lorraine Cross
• Lo Shu
• Lotka-Volterra Equations
• Low-Dimensional Topology
• Lower Bound
• Lower Denjoy Sum
• Lower Integral
• Lower Limit
• Lower Sum
• Lower-Trimmed Subsequence
• Lowest Terms Fraction
• Loxodrome
• Lozenge
• Lozenge Method