 ##  [Analytic Continuation](/analytic-continuation) 

  ##  [Analytic Continuation](https://natural.quantumdictionary.io/analytic-continuation-0) 

  
 [![Natural & Formal Sciences Dictionary](/sites/default/files/styles/large/public/2026-01/Natural%20%26%20Formal%20Sciences.png.webp?itok=2kCDRVQv)](/topic-specific-dictionaries/natural-formal-sciences)


**Natural &amp; Formal Sciences Dictionary**

 
Definition

The process of extending a holomorphic function from an initial domain to a larger domain by uniquely patching overlapping power-series or local representations, continuing along paths until an obstruction is reached.

 
 ##  [Analytic Continuation](https://mathlogic.quantumdictionary.io/analytic-continuation-1) 

  
 [![Mathematics & Logic Dictionary](/sites/default/files/styles/large/public/2026-01/Mathematics%20%26%20Logic.png.webp?itok=UhtTRPnp)](/topic-specific-dictionaries/natural-formal-sciences/mathematics-logic)

- Natural &amp; Formal Sciences -

**Mathematics &amp; Logic Dictionary**

 
Definition

The process of extending the domain of a holomorphic (analytic) function beyond its original region by defining it on larger domains so that on overlaps the extension agrees with the original function; extensions are unique when connectedness and analyticity conditions hold.

 
 ##  [Analytic Continuation](https://puremath.quantumdictionary.io/analytic-continuation-2) 

  
 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics &amp; Logic -

**Pure Mathematics Dictionary**

 
Definition

The process of extending a holomorphic (complex-analytic) function from its original domain to a larger connected region by using the unique continuation properties of analytic functions, typically by continuing power series or values along paths.