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, ...
– 14 August 1886, Bar-le-Duc) 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, mathematical structure, structure, space, Mathematica ...
and a member of the
Académie des sciences
The French Academy of 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 method, scientific research. It was at the forefron ...
(1885). His main works were in the areas of
geometry
Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...
and
complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic ...
. 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
In mathematics, orthogonality (mathematics), orthogonality is the generalization of the geom ...
(see
Laguerre polynomials
In mathematics, the Laguerre polynomials, named after Edmond Laguerre (1834–1886), are nontrivial solutions of Laguerre's differential equation:
xy'' + (1 - x)y' + ny = 0,\
y = y(x)
which is a second-order linear differential equation. Thi ...
).
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 numerical analysis, a root-finding algorithm is an algorithm for finding zeros, also called "roots", of continuous functions. A zero of a function is a number such that . As, generally, the zeros of a function cannot be computed exactly nor ...
tailored to
polynomial
In mathematics, a polynomial is a Expression (mathematics), mathematical expression consisting of indeterminate (variable), indeterminates (also called variable (mathematics), variables) and coefficients, that involves only the operations of addit ...
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 Laguerre ...
), including the
Laguerre transformation
The Laguerre transformations or axial homographies are an analogue of Möbius transformations over the dual numbers. Originally published as ''Kompleksnye Chisla i Ikh Primenenie v Geometrii'' (in Russian). Moscow: Fizmatgiz. 1963 When studying th ...
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 that searches the full text of books and magazines that Google has scanned, converted to text using optical charac ...
*
*
Oeuvres de Laguerrepubl. sous les auspices de l'Académie des sciences par MM.
Charles Hermite
Charles Hermite () FRS FRSE MIAS (24 December 1822 – 14 January 1901) was a French mathematician who did research concerning number theory, quadratic forms, invariant theory, orthogonal polynomials, elliptic functions, and algebra.
Hermite p ...
,
Henri Poincaré
Jules Henri Poincaré (, ; ; 29 April 185417 July 1912) was a French mathematician, Theoretical physics, theoretical physicist, engineer, and philosophy of science, philosopher of science. He is often described as a polymath, and in mathemati ...
, 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, ...
*
''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
*
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 associated with a vector space. Tenso ...
*
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 Laguerre ...
*
Laguerre polynomials
In mathematics, the Laguerre polynomials, named after Edmond Laguerre (1834–1886), are nontrivial solutions of Laguerre's differential equation:
xy'' + (1 - x)y' + ny = 0,\
y = y(x)
which is a second-order linear differential equation. Thi ...
*
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 nont ...
*
Laguerre transformations
*
Laguerre's theorem
*
Laguerre–Forsyth invariant In projective 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 Forsyth, the latter of whom analyzed the invariant in an influential book ...
*
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
Academic staff of the Collège de France
Members of the French Academy of Sciences
19th-century French mathematicians