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...

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

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

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...

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...

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

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...

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

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...

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...

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

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...

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...

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...

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

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

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

{-\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...

non-positive integer, then Kummer's function (if it is defined) is a generalized Laguerre polynomial. Just as the confluent differential equation is a limit of 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...

{\displaystyle [-1,1]} . The Laguerre polynomials are orthogonal with respect to the exponential distribution. Somewhat more general Laguerre polynomial sequences...

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

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

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

Jacques Miquelon, Canadian lawyer and judge (born 1911) 2005 – Enrique Laguerre, Puerto Rican-American author and critic (born 1906) 2008 – Mario Rigoni...