Complex analysis: Cauchy integral theorem and residues
Análisis complejo: teorema integral de Cauchy y residuos
- Date
- 1825 · confidence high
- Place
- Paris, France
- Credited to
- Augustin-Louis Cauchy; extended by Riemann (1851) and Weierstrass
- People
- 👤 Augustin Louis Cauchy1789–1857👤 Karl Weierstraß1815–1897
- Field
- Knowledge & symbols
What was discovered
The integral of a holomorphic function along a closed path is zero, and integrals are calculated by residues at singularities. It turns functions of a complex variable into the most powerful instrument of analysis.
Gauss knew the integral theorem in 1811 but did not publish it.
What it led to
- the Riemann zeta function
- Riemann surfaces
- the prime number theorem
- integral transforms
Built on
- Euler formula and Euler identity1748
- Abel and Jacobi's elliptic functions
Made possible
- Riemann hypothesis1859
- aerodynamics (conformal mapping)
- circuit theory
- signal processing