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The 27 pages that link to Contour integration, each with the reason it gives.

• Holomorphic functionRelated: Holomorphicity enables powerful integral theorems for contours and their interiors.

• Complex analysisBroader topic: Integrating along closed curves is the starting point for Cauchy’s integral theorem.

• Cauchy's integral formulaNarrower topic: The formula’s boundary data are integrated along an oriented contour.

• Improper integralCompared with: Contour integration can bypass real-axis singularities rather than define them by real one-sided limits.

• Laurent seriesRelated: Integrating a Laurent series around a circle isolates its inverse-first-power coefficient.

• Meromorphic functionRelated: Poles inside a contour often let integrals be evaluated through residues.

• Line integralRelated: It is the complex-analysis counterpart, often exploiting analyticity and closed contours.

• IntegralBroader topic: It replaces an interval of real inputs with a path through the complex plane.

• Complex logarithmRelated: Logarithmic branches affect whether an integrand can remain analytic along a contour.

• Residue theoremRelated: The theorem concerns integrals over closed contours.

• Surface integralCompared with: Despite similar terminology, it is a curve integral, not a surface integral.

• Winding numberNarrower topic: Integrating dz/(z−a) around a curve gives 2πi times its winding number about a.

• Argument principleRelated: The theorem can be expressed as a contour integral of the logarithmic derivative.

• Explicit formulaRelated: Shifting contours picks up residues at zeros and poles, producing the formula’s terms.

• ResidueNarrower topic: Residues determine contour integrals when the contour encloses isolated singularities.

• Cauchy estimatesNarrower topic: The contour integral is the operation whose length and denominator produce the bound.

• Cauchy's integral theoremNarrower topic: The theorem asserts that this integral is zero for eligible closed contours.

• Integral calculusBroader topic: It generalizes integration from real intervals to paths in a complex domain.

• Integration by partsCompared with: It can evaluate real integrals through complex analysis rather than repeated real-variable integration by parts.

• Closed curveRelated: Closed contours let integral theorems relate boundary values to singularities inside.

• Indefinite integralCompared with: Its path-based definition differs from the real-variable antiderivative notation.

• Rouché's theoremNarrower topic: The argument-principle integral converts boundary behavior into an interior zero count.

• Jordan's lemmaNarrower topic: Jordan's lemma supplies an estimate for one part of a closed contour.

• Integration by substitutionCompared with: It changes the integration path in a complex domain, unlike ordinary real-variable substitution.

• Volume integralCompared with: Its domain is a contour, unlike the three-dimensional domain here.

• Estimation lemmaNarrower topic: The lemma bounds this integral by controlling the integrand and the curve’s length.

• Limits of integrationCompared with: Its path, rather than two real interval endpoints alone, specifies where integration occurs.