gaussische

Gaussische is the German adjectival form derived from the name Gauss, used to describe concepts connected with the mathematician Carl Friedrich Gauss or with Gaussian functions and distributions. In German-language technical writing the term appears in many compound forms that denote Gaussian-related ideas.

Common examples include Gaußsche Verteilung (Gaussian distribution), Gaußsche Glockenkurve (Gaussian bell curve), Gaußsche Funktion (Gaussian function), Gaußsches Integral (Gaussian integral), and Gaußsche Unschärfe (Gaussian blur) in image processing. These terms reflect the central role of Gaussian shapes and statistics in mathematics, physics, statistics, and engineering.

The gaussische family centers on the Gaussian or normal distribution, which models numerous natural phenomena and measurement errors. The Gaussian function describes a bell-shaped curve given by a exponential form and serves as a building block in probability, statistics, and analysis. The Gaussian integral expresses the fundamental integral of the Gaussian function and yields the constant sqrt(pi). In numerical methods and linear algebra, the related Gaußsche Eliminationsverfahren (Gaussian elimination) provides a standard method for solving systems of linear equations. In applied fields, gaussische terminology also covers image and signal processing techniques that rely on Gaussian kernels for smoothing or noise modeling.

Overall, gaussische terms form a coherent family in German technical language, signaling properties or results associated with Gaussian concepts and the legacy of Gauss across disciplines. The corresponding English terms are Gaussian or Gauss-related, but the German form remains widely used in literature and teaching.