analytic continuation
"Analytic continuation" is crucial in complex analysis for extending the domain of analytic functions, enabling deeper exploration of their properties.
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Definition
C2Complex Analysis
(technical, academic)A method for extending the domain of an analytic function to a larger domain while preserving its analytic properties.
Example
- The Riemann zeta function can be extended to the entire complex plane except for a singularity at s=1 through analytic continuation.
- Using analytic continuation, the square root function can be extended around the origin, resulting in a multivalued function.
Similar
Terms that have similar or relatively close meanings to "analytic continuation":