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* The point ''a'' is a [[removable singularity]] of ''f'' if there exists a [[holomorphic function]] ''g'' defined on all of ''U'' such that ''f''(''z'') = ''g''(''z'') for all ''z'' in ''U'' \ {''a''}. The function ''g'' is a continuous replacement for the function ''f''.<ref>{{Cite web|url=http://mathworld.wolfram.com/Singularity.html|title=Singularity|last=Weisstein|first=Eric W.|website=mathworld.wolfram.com|language=en|access-date=2019-12-12}}</ref>

* The point ''a'' is a [[removable singularity]] of ''f'' if there exists a [[holomorphic function]] ''g'' defined on all of ''U'' such that ''f''(''z'') = ''g''(''z'') for all ''z'' in ''U'' \ {''a''}. The function ''g'' is a continuous replacement for the function ''f''.<ref>{{Cite web|url=http://mathworld.wolfram.com/Singularity.html|title=Singularity|last=Weisstein|first=Eric W.|website=mathworld.wolfram.com|language=en|access-date=2019-12-12}}</ref>

如果在所有“U”上定义了一个[[全纯函数]]“g”，则点“a”是“f”的[[可移动奇点]]“g”，使得“U”\{“a”}中所有“z”的“f”（“z”）=“g”（“z”）。函数“g”是函数“f”的连续替换

如果存在一个定义在所有U上的全纯函数g，使得对于U \ {a}中的所有z, f(z) = g(z)，那么点a是f的一个可去奇点。函数g是函数f的连续替换。<ref>{{Cite web|url=http://mathworld.wolfram.com/Singularity.html|title=Singularity|last=Weisstein|first=Eric W.|website=mathworld.wolfram.com|language=en|access-date=2019-12-12}}</ref>

* The point ''a'' is a [[pole (complex analysis)|pole]] or non-essential singularity of ''f''  if there exists a holomorphic function ''g'' defined on ''U'' with ''g''(''a'') nonzero, and a [[natural number]] ''n'' such that ''f''(''z'') = ''g''(''z'') / (''z'' − ''a'')^''n'' for all ''z'' in ''U'' \ {''a''}. The least such number ''n'' is called the ''order of the pole''. The derivative at a non-essential singularity itself has a non-essential singularity, with ''n'' increased by 1 (except if ''n'' is 0 so that the singularity is removable).

* The point ''a'' is a [[pole (complex analysis)|pole]] or non-essential singularity of ''f''  if there exists a holomorphic function ''g'' defined on ''U'' with ''g''(''a'') nonzero, and a [[natural number]] ''n'' such that ''f''(''z'') = ''g''(''z'') / (''z'' − ''a'')^''n'' for all ''z'' in ''U'' \ {''a''}. The least such number ''n'' is called the ''order of the pole''. The derivative at a non-essential singularity itself has a non-essential singularity, with ''n'' increased by 1 (except if ''n'' is 0 so that the singularity is removable).

如果存在定义在“U”上的全纯函数“g”，且“g”（“a”）非零，且存在一个[[自然数]]“n”，使得“f”（“z”）=“g”（“z”）/（“z”-“a”）中的所有“z”，则点“a”为[[极点（复分析）|极]]或“f”的非本质奇点。最小的这个数“n”称为“极序”。非本质奇点处的导数本身具有非本质奇点，“n”增加1（除非“n”为0，因此奇点可移除）

如果存在定义在“U”上的全纯函数“g”，且“g”（“a”）非零，且存在一个自然数“n”，使得对所有“z”属于“U”\{“a”},“f”（“z”）=“g”（“z”）/ (“z” – “a”)n，则点“a”为[[极点（复分析）|极]]或“f”的<font color=“#ff8000”>非本质奇点 non-essential singularity</font>。最小的这个数“n”称为“极序”。 <font color=“#ff8000”>非本质奇点</font>处的导数本身也有一个<font color=“#ff8000”>非本质奇点</font>，当“n”增加1时（除非“n”为0，因此<font color=“#ff8000”>奇点</font>可移除）

* The point ''a'' is an [[essential singularity]] of ''f'' if it is neither a removable singularity nor a pole. The point ''a'' is an essential singularity [[iff|if and only if]] the [[Laurent series]] has infinitely many powers of negative degree.<ref name=":1" />

* The point ''a'' is an [[essential singularity]] of ''f'' if it is neither a removable singularity nor a pole. The point ''a'' is an essential singularity [[iff|if and only if]] the [[Laurent series]] has infinitely many powers of negative degree.<ref name=":1" />

如果点“a”既不是可移动奇点，也不是极点，则它是“f”的[[基本奇点]]。点“a”是本质奇点[[iff |当且仅当][[Laurent级数]]具有无穷多个负次幂。

如果点“a”既不是可去奇点，也不是极点，则它是“f”的 <font color=“#ff8000”>非本质奇点</font>。点“a”是 <font color=“#ff8000”>非本质奇点</font>[[iff |当且仅当][[Laurent级数]]具有无穷多个负次幂。