In mathematics, specifically in complex analysis, Cauchy's estimate gives local bounds for the derivatives of a holomorphic function. These bounds are...

In mathematics, Cauchy's integral formula, named after Augustin-Louis Cauchy, is a central statement in complex analysis. It expresses the fact that a...

integrals and infinite series as well. It generalizes the Cauchy integral theorem and Cauchy's integral formula. The residue theorem should not be confused...

like a Cauchy distribution. Because the parameters of the Cauchy distribution do not correspond to a mean and variance, attempting to estimate the parameters...

Antiderivative (complex analysis) Antiholomorphic function Biholomorphy Cauchy's estimate Harmonic maps Harmonic morphisms Holomorphic separability Meromorphic...

|z|=r} on the circle C r {\displaystyle C_{r}} . (This estimate is known as Cauchy's estimate.) But the choice of r {\displaystyle r} in the above is...

f : U → C using Cauchy's integral formula as follows. Let r > 0 such that the closed disk B(z, r) ∪ S(z, r) is contained in U. Then Cauchy's integral formula...

made when the functions are holomorphic. One can use, for instance, Cauchy's estimate to show the equicontinuity (on a compact subset) and conclude that...

the Cauchy product is the discrete convolution of two infinite series. It is named after the French mathematician Augustin-Louis Cauchy. The Cauchy product...

{\displaystyle t=0} . Cauchy's mean value theorem can be used to prove L'Hôpital's rule. The mean value theorem is the special case of Cauchy's mean value theorem...