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Edmond Nicolas Laguerre (9 April 1834,
Bar-le-Duc Bar-le-Duc (), formerly known as Bar, is a commune in the Meuse département, of which it is the capital. The department is in Grand Est in northeastern France. The lower, more modern and busier part of the town extends along a narrow valley, s ...
– 14 August 1886,
Bar-le-Duc Bar-le-Duc (), formerly known as Bar, is a commune in the Meuse département, of which it is the capital. The department is in Grand Est in northeastern France. The lower, more modern and busier part of the town extends along a narrow valley, s ...
) was a French
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History O ...
and a member of the
Académie des sciences The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research. It was at the ...
(1885). His main works were in the areas of
geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ...
and complex analysis. He also investigated
orthogonal polynomials In mathematics, an orthogonal polynomial sequence is a family of polynomials such that any two different polynomials in the sequence are orthogonal to each other under some inner product. The most widely used orthogonal polynomials are the clas ...
(see
Laguerre polynomials In mathematics, the Laguerre polynomials, named after Edmond Laguerre (1834–1886), are solutions of Laguerre's equation: xy'' + (1 - x)y' + ny = 0 which is a second-order linear differential equation. This equation has nonsingular solutions only ...
).
Laguerre's method In numerical analysis, Laguerre's method is a root-finding algorithm tailored to polynomials. In other words, Laguerre's method can be used to numerically solve the equation for a given polynomial . One of the most useful properties of this metho ...
is a
root-finding algorithm In mathematics and computing, a root-finding algorithm is an algorithm for finding zeros, also called "roots", of continuous functions. A zero of a function , from the real numbers to real numbers or from the complex numbers to the complex numbe ...
tailored to
polynomial In mathematics, a polynomial is an expression (mathematics), expression consisting of indeterminate (variable), indeterminates (also called variable (mathematics), variables) and coefficients, that involves only the operations of addition, subtrac ...
s. He laid the foundations of a geometry of oriented spheres (Laguerre geometry and
Laguerre plane In 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 after the French mathematician Edmond Nicolas Laguerre. The classical Laguerr ...
), including the
Laguerre transformation Edmond Nicolas Laguerre (9 April 1834, Bar-le-Duc – 14 August 1886, Bar-le-Duc) was a French mathematician and a member of the Académie des sciences (1885). His main works were in the areas of geometry and complex analysis. He also investiga ...
or transformation by reciprocal directions.


Works


Selection

* * * *
Théorie des équations numériques
', Paris: Gauthier-Villars. 1884 on
Google Books Google Books (previously known as Google Book Search, Google Print, and by its code-name Project Ocean) is a service from Google Inc. that searches the full text of books and magazines that Google has scanned, converted to text using optical ...
* *
Oeuvres de Laguerre
publ. sous les auspices de l'Académie des sciences par MM. Charles Hermite,
Henri Poincaré Jules Henri Poincaré ( S: stress final syllable ; 29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science. He is often described as a polymath, and in mathematics as "The ...
, et
Eugène Rouché Eugène Rouché (18 August 1832 – 19 August 1910) was a French mathematician. Career He was an alumnus of the École Polytechnique, which he entered in 1852. He went on to become professor of mathematics at the Charlemagne lyceum then at the ...
.'' (Paris, 1898-1905) (reprint: New York : Chelsea publ., 1972 )


Extensive lists


More than 80 articles
on Nundam.org.p


See also

*
Isotropic line In the geometry of quadratic forms, an isotropic line or null line is a line for which the quadratic form applied to the displacement vector between any pair of its points is zero. An isotropic line occurs only with an isotropic quadratic form, an ...
* ''q''-Laguerre polynomials * Big ''q''-Laguerre polynomials * Discrete Laguerre polynomials *
Gauss–Laguerre quadrature In numerical analysis Gauss–Laguerre quadrature (named after Carl Friedrich Gauss and Edmond Laguerre) is an extension of the Gaussian quadrature method for approximating the value of integrals of the following kind: :\int_^ e^ f(x)\,dx. In thi ...
*
Laguerre-Gaussian modes In optics, a Gaussian beam is a beam of electromagnetic radiation with high monochromaticity whose amplitude envelope in the transverse plane is given by a Gaussian function; this also implies a Gaussian intensity (irradiance) profile. Thi ...
*
Laguerre form In mathematics, the Laguerre form is generally given as a third degree tensor In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors ma ...
*
Laguerre formula The Laguerre formula (named after Edmond Laguerre) provides the acute angle \phi between two proper real lines, as follows: :\phi=, \frac \operatorname \operatorname(I_1,I_2,P_1,P_2), where: * \operatorname is the principal value of the complex ...
* Laguerre group *
Laguerre's method In numerical analysis, Laguerre's method is a root-finding algorithm tailored to polynomials. In other words, Laguerre's method can be used to numerically solve the equation for a given polynomial . One of the most useful properties of this metho ...
*
Laguerre–Pólya class The Laguerre–Pólya class is the class of entire functions consisting of those functions which are locally the limit of a series of polynomials whose roots are all real.
*
Laguerre plane In 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 after the French mathematician Edmond Nicolas Laguerre. The classical Laguerr ...
*
Laguerre polynomials In mathematics, the Laguerre polynomials, named after Edmond Laguerre (1834–1886), are solutions of Laguerre's equation: xy'' + (1 - x)y' + ny = 0 which is a second-order linear differential equation. This equation has nonsingular solutions only ...
*
Laguerre transform In mathematics, Laguerre transform is an integral transform named after the mathematician Edmond Laguerre, which uses generalized Laguerre polynomials In mathematics, the Laguerre polynomials, named after Edmond Laguerre (1834–1886), are solut ...
*
Laguerre transformations Edmond Nicolas Laguerre (9 April 1834, Bar-le-Duc – 14 August 1886, Bar-le-Duc) was a French mathematician and a member of the Académie des sciences (1885). His main works were in the areas of geometry and complex analysis. He also investigate ...
* Laguerre's theorem * Laguerre–Forsyth invariant * Laguerre–Samuelson inequality * Laguerre–Voronoi diagram


References

*
Nécrologie
. In: ''
Nouvelles annales de mathématiques The ''Nouvelles Annales de Mathématiques'' (subtitled ''Journal des candidats aux écoles polytechnique et normale'') was a French scientific journal in mathematics. It was established in 1842 by Olry Terquem and Camille-Christophe Gerono, and c ...
'', 3rd series, vol. 8 (1889), p. 494–496—Obituary


External links

* {{DEFAULTSORT:Laguerre, Edmond Nicolas 1834 births 1886 deaths People from Bar-le-Duc École Polytechnique alumni Collège de France faculty Members of the French Academy of Sciences 19th-century French mathematicians