Linked from

The 13 pages that link to Cauchy principal value, each with the reason it gives.

• Definite integralCompared with: It can exist even when an ordinary improper integral diverges.

• Improper integralCompared with: Symmetric cancellation can produce a principal value without making the improper integral converge.

• Riemann integralCompared with: It can assign a finite value where the corresponding improper integral diverges.

• Residue theoremCompared with: Principal values can arise when contour methods encounter singularities on the integration path.

• Contour integrationRelated: Indented contours relate principal-value integrals to residues at boundary poles.

• ResidueCompared with: It addresses contour singularities on the path rather than extracting a local Laurent coefficient.

• Distribution theoryBroader topic: The Cauchy principal value of one over x defines a distribution despite its singularity.

• Fourier inversion theoremCompared with: Some inversion formulas require a principal value rather than an ordinary convergent integral.

• Jordan's lemmaRelated: Oscillatory contour integrals with real-axis poles often require this interpretation.

• Iterated integralCompared with: It can assign a value where ordinary improper integration fails, so order comparisons require care.

• Hilbert transformRelated: The kernel is singular at zero, so this limiting prescription defines the transform.

• Limits of integrationCompared with: It handles some divergent integrals through a limiting rule not captured by ordinary endpoint evaluation.

• Exponential integralRelated: The real definition of Ei across its pole uses this limiting prescription.