singularity in function

Function can have points {singularity, function} where it has multiple values {degeneracy, function} and so is not a function.

boundary

Line can have all or many singular points {natural boundary}.

types

Polynomial functions can go to infinity {pole, singularity}. Function main term can have form ln(x) {logarithmic singularity} {logarithmic branch point}. Function can go to infinity but have bound {removable singularity}. Pole, logarithmic singularity, removable singularity, and essential singularity have no other singularities nearby {isolated singularity}. f(x) * (x - c)^n, where n is integer greater than 0, can be not differentiable {essential singularity}.

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3-Algebra-Function

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Date Modified: 2022.0224