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The 33 pages that link to Analytic continuation, each with the reason it gives.

• Riemann zeta functionRelated: It extends ζ(s) beyond the half-plane where its defining series converges.

• Riemann hypothesisRelated: It defines the zeta function where the nontrivial zeros relevant to the hypothesis occur.

• Gamma functionNarrower topic: It extends the integral-defined gamma function to the complex plane, except at its poles.

• Laurent seriesRelated: Expansions on different annuli describe a function across regions separated by singularities.

• Radius of convergenceRelated: Continuation can extend a function beyond a particular Taylor series’ disk of convergence.

• Identity theoremRelated: Any two continuations agreeing on an overlapping open region must agree throughout their connected overlap.

• Entire functionRelated: An entire function already provides a single-valued continuation across the entire finite plane.

• Cauchy problemRelated: For analytic elliptic equations, Cauchy data may determine a local solution through continuation despite instability.

• Complex logarithmRelated: Continuing a logarithm around zero can return a different value after one circuit.

• Riemann surfaceRelated: Continuing a function around loops reveals why its natural domain may need multiple sheets.

• Dirichlet L-functionRelated: Continuation gives these functions meaning outside the half-plane of absolute convergence.

• Dirichlet seriesRelated: Many Dirichlet series acquire meaning beyond the half-plane where their sums converge.

• Cauchy principal valueCompared with: It can assign regularized values by continuation, a distinct procedure from principal-value limits.

• Jacques HadamardRelated: Continuing the zeta function reveals the analytic information needed in Hadamard’s prime-number argument.

• Rational approximationRelated: Rational forms can reveal behavior beyond a function’s local power-series region.

• Dedekind zeta functionRelated: The defining series converges only in a half-plane, while the completed function extends much farther.

• Generalized Riemann hypothesisRelated: The relevant zeros lie beyond the original convergence region of many L-series.

• Padé approximantRelated: Padé approximants can estimate function values outside a power series' disk of convergence.

• Removable singularityRelated: Removing a singular point is a local instance of extending an analytic function.

• Beta functionRelated: It extends the integral-defined beta function to most complex argument pairs.

• Branch pointRelated: Continuation along loops encircling a branch point can return a different function value.

• Abel's theorem (power series)Related: Boundary limits can identify values where a series representation itself stops converging beyond the boundary.

• Hadamard three-circle theoremRelated: Quantitative bounds across nested circles help describe how analytic information continues through an annulus.

• Algebraic functionRelated: Continuation tracks an algebraic function branch along paths in the input plane.

• Hartogs extension theoremRelated: Hartogs extension is a forced continuation across certain missing sets.

• Schwarz reflection principleNarrower topic: Reflection is a concrete method of analytic continuation across certain boundaries.

• Gösta Mittag-LefflerRelated: It is a central technique in the complex analysis that shaped his research.

• Weierstrass preparation theoremRelated: The theorem arose within the theory of local analytic functions and their behavior.

• Hadamard gap theoremCompared with: The theorem rules out continuation through every point of the specified circle.

• Phragmén–Lindelöf principleRelated: Growth bounds can limit how continued functions behave in large complex domains.

• Analytic functionRelated: Overlapping local power series can extend a function into a larger domain.

• Analyticity of holomorphic functionsRelated: Overlapping local power series can extend a function beyond one expansion disk.

• Dixon's identityRelated: Continuation can extend identities beyond the parameter region where the original sum converges.