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单词 Singular Point (Function)
释义

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.

See also Essential Singularity, Irregular Singularity, Ordinary Point, Pole, Regular SingularPoint, Removable Singularity, Singular Point (Differential Equation)


References

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


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