mathematics, a Laguerre plane is one of the three types of Benz plane, which are the Möbius plane, Laguerre plane and Minkowski plane. Laguerre planes are named...

Laguerre form Laguerre formula Laguerre group Laguerre's method Laguerre–Pólya class Laguerre plane Laguerre polynomials Laguerre transform Laguerre transformations...

geometry is called a Laguerre plane. Collectively these planes are sometimes referred to as Benz planes. A topological Benz plane is classical, if each...

were introduced separately: Möbius planes, Laguerre planes, and Minkowski planes. Starting from the real Euclidean plane and merging the set of lines with...

geometry are finite Möbius or inversive planes and Laguerre planes, which are examples of a general type called Benz planes, and their higher-dimensional analogs...

as the classical Möbius plane. It is one of the Benz planes: Möbius plane, Laguerre plane and Minkowski plane. Affine planes are systems of points and...

solved using the Laguerre-Gaussian modal decomposition. These functions are written in cylindrical coordinates using generalized Laguerre polynomials. Each...

mathematics, a Minkowski plane (named after Hermann Minkowski) is one of the Benz planes (the others being Möbius plane and Laguerre plane). Applying the pseudo-euclidean...

oriented lines on the plane. The Laguerre transformations map lines to lines, and include in particular all isometries of the plane. Strictly speaking,...

directions or Laguerre inversion, being a generator of the Laguerre group. It transforms not only spheres into spheres but also planes into planes. If time...

bars is a real number. Laguerre formula can be useful in computer vision, since the absolute conic has an image on the retinal plane which is invariant under...

geometry are finite Möbius or inversive planes and Laguerre planes, which are examples of a general type called Benz planes, and their higher-dimensional analogs...

In computational geometry, a power diagram, also called a Laguerre–Voronoi diagram, Dirichlet cell complex, radical Voronoi tesselation or a sectional...

Erich, Planar Circle Geometries, an Introduction to Moebius-, Laguerre- and Minkowski Planes (PDF), retrieved 20 September 2014 (PDF; 891 kB). Katz, Victor...

geometry, the Laguerre–Forsyth invariant is a cubic differential that is an invariant of a projective plane curve. It is named for Edmond Laguerre and Andrew...

equivalently described as a superposition of Hermite-Gaussian modes or Laguerre-Gaussian modes which are described below). Modes in waveguides can be classified...

and never with a definite quadratic form. Using complex geometry, Edmond Laguerre first suggested the existence of two isotropic lines through the point...

and the ovoid is a quadric. There are Möbius planes, which are not ovoidal. For ovoidal Laguerre planes there exists a bundle theorem with an analogous...

Moebius-, Laguerre- and Minkowski Planes, S. 33, (PDF; 757 kB) Lecture Note Planar Circle Geometries, an Introduction to Moebius-, Laguerre- and Minkowski...

generalized Laguerre differential equation, which has known solutions: the generalized Laguerre functions. Then we normalize the generalized Laguerre functions...

Introduction to Moebius-, Laguerre- and Minkowski Planes (PDF; 891 kB), Uni Darmstadt, S. 29–35. How to Project Spherical Conics into the Plane by Yoichi Maeda...

}J_{\alpha }(z),} where L(α) n is the Laguerre function. Using the expressions equivalating Hermite polynomials and Laguerre polynomials where two equations...

divides the plane into regions within which the circle minimizing the power is constant. More generally, French mathematician Edmond Laguerre defined the...

the nth-order Hermite function is related to the nth-order Laguerre polynomial. The Laguerre polynomials are L n ( x ) := ∑ k = 0 n ( n k ) ( − 1 ) k k...

classical orthogonal polynomials, consisting of the Hermite polynomials, the Laguerre polynomials and the Jacobi polynomials. The Gegenbauer polynomials form...

elements in R2 and R4; treating them using linear combinations goes back to Laguerre in 1867, who also defined systems of linear equations. In 1857, Cayley...

Laguerre- and Minkowski-planes, p. 36. E. Hartmann, Lecture Note Planar Circle Geometries, an Introduction to Möbius-, Laguerre- and Minkowski Planes...

Hartmann: Planar Circle Geometries, an Introduction to Moebius-, Laguerre- and Minkowski Planes. Skript, TH Darmstadt (PDF; 891 kB), p. 45. F. Buekenhout: Plans...

Computer-generated holograms (CGHs) are the calculated interferogram between a plane wave and a Laguerre-Gaussian beam which is transferred to film. The CGH resembles...

{-\log(E(z))}{z}}\geq 0} (in the UHP). A smaller class of entire functions is the Laguerre–Pólya class, which consists of those functions which are locally the limit...