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 Laguerrepubl. 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 articleson 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
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{{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