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Cauchy sequenceIn mathematical analysis, a Cauchy sequence is a sequence whose terms become arbitrarily close to each other as the sequence progresses. They are named after the French mathematician Augustin Louis Cauchy. They are of interest because, given certain condi Cauchy distributionThe Cauchy distribution is a probability distribution with probability density function : where x is the location parameter and s is the scale parameter''. The special case when x 0 and s 1 is called the standard Cauchy distribution with the probability d Cauchy-Riemann equationsPartial differential equations Complex analysis In complex analysis, the Cauchy-Riemann differential equations are two partial differential equations which provide a necessary and sufficient condition for a function to be holomorphic. Let f u + iv be a fu Cauchy-Schwarz inequalityIn mathematics, the Cauchy-Schwarz inequality also known as the Schwarz inequality or the Cauchy-Bunyakovski-Schwarz inequality is a useful inequality encountered in many different settings, such as linear algebra applied to vectors, in analysis applied t Cauchy integral theoremComplex analysis Theorems The Cauchy integral theorem in complex analysis is an important statement about path integrals for holomorphic functions in the complex plane. Essentially, it says that if two different paths connect the same two points, and a fu Cauchy's integral formulaCauchy's integral formula is a central statement in complex analysis. It expresses the fact that a holomorphic function defined on a disk is completely determined by its values on the boundary of the disk. It can also be used to formulate integral formula Cauchy-Binet formula Cauchy-à-la-Tour Cauchy principal value Cauchy horizon Cauchy product Cauchy (crater) Cauchy space Cauchy-Euler equation