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.
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