Let be a domain, , and let be holomorphic. If the Laurent series expansion of around contains infinitely many terms with negative powers of , then is said to be an essential singularity of . Any singularity of is a removable singularity, a pole or an essential singularity.
If is an essential singularity of , then the image of any punctured neighborhood of under is dense in (the Casorati-Weierstrass theorem). In fact, an even stronger statement is true: according to Picard’s theorem, the image of any punctured neighborhood of is , with the possible exception of a single point.
|Date of creation||2013-03-22 13:32:10|
|Last modified on||2013-03-22 13:32:10|
|Last modified by||pbruin (1001)|