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(xn) is Cauchy when abs(xn-xm) tends to 0 as m,n tend to infinity.
The Cauchy or Cauchy-Lorentz distribution. The ratio of two Normal random variables has a C-L distribution.
It is a Scientist's last name. Augustin-Jean Fresnel, born 1788, died 1827
Well, cauchy-riemann differential equation is a part of complex variables and in real-life applications such as engineering, it can be used in determining the flow of fluids, such as the flow around the pipe. In fluid mechanics, the cauchy-riemann equations are decribed by two complex variables, i.e. u and v, and if these two variables satisfy the equations in an open subset of R2, then the vector field can be asserted from the two cauchy-riemann equations, ux = vy (1) uy = - vx (2) This I think can help interpreting the potential flow (Wikipedia) in two dimensions using the cauchy-riemann equations. In fluid mechanics, the potential flow can be analyzed using the cauchy-riemann equations.
Maximum likelihood estimators of the Cauchy distribution cannot be written in closed form since they are given as the roots of higher-degree polynomials. Please see the link for details.