meromorphic extension

Let $A\\subset B\\subseteq\\mathbb{C}$ and $f\\colon A\\to\\mathbb{C}$ be analytic. A meromorphic extension of $f$ is a meromorphic function $g\\colon B\\to\\mathbb{C}$ such that $g|_{A}=f$ .

The meromorphic extension of an analytic function to a larger domain (http://planetmath.org/Domain) is unique; i.e. (http://planetmath.org/Ie), using the above notation, if $h\\colon B\\to\\mathbb{C}$ has the property that $h|_{A}=f$ , then $g=h$ on $B$ .

Occasionally, an analytic function and its meromorphic extension are denoted using the same notation. A common example of this phenomenon is the Riemann zeta function.

单词	MeromorphicExtension
释义	meromorphic extension Let $A\\subset B\\subseteq\\mathbb{C}$ and $f\\colon A\\to\\mathbb{C}$ be analytic. A meromorphic extension of $f$ is a meromorphic function $g\\colon B\\to\\mathbb{C}$ such that $g\|_{A}=f$ . The meromorphic extension of an analytic function to a larger domain (http://planetmath.org/Domain) is unique; i.e. (http://planetmath.org/Ie), using the above notation, if $h\\colon B\\to\\mathbb{C}$ has the property that $h\|_{A}=f$ , then $g=h$ on $B$ . Occasionally, an analytic function and its meromorphic extension are denoted using the same notation. A common example of this phenomenon is the Riemann zeta function.
随便看	SupplementaryAngles supplementary angles SupplementaryChords supplementary chords Support support support support Support1 Support12 SupportgradedRing support (graded ring) SupportOfFunction support of function SupportOfIntegrableFunctionIssigmafinite support of integrable function is σ-finite SupportOfIntegrableFunctionWithRespectToCountingMeasureIsCountable support of integrable function with respect to counting measure is countable SuppressionOfScience suppression of science Supremum supremum SupremumOverClosure supremum over closure SuranyisTheorem