 |
|
| |
|
||||
Legendre polynomials (4048 bytes)
1: ...d (wrongly) to indicate the [[associated Legendre polynomials]].'' 3: ...s]], '''Legendre functions''' are solutions to '''Legendre's differential equation''': 7: They are named after [[Adrien-Marie Legendre]]. This [[differential equation|ordinary differen... 9: ... a [[polynomial sequence]] called the '''Legendre polynomials'''. 11: Each Legendre polynomial P<sub>''n''</sub>(''x'') is an ''n''th... Associated Legendre polynomials (1240 bytes) 1: ...ndre polynomials]]''', named after [[Adrien-Marie Legendre]], are defined by: 5: These differ from the [[Legendre polynomials]]. 13: ...a</math>, the Associated Legendre polynomials are polynomials of <math>\cos\theta \ \ , \ \ \sin\theta</math>. 15: The Associated Legendre polynomials are an important part of [[spherical harmonic]]s. 20: * [[Legendre polynomials]]. Legendre form (417 bytes) 1: In [[mathematics]], the '''Legendre forms of [[elliptic integral]]s''', ''F''(φ,'... Legendre (crater) (2627 bytes) 20: |[[Adrien Marie Legendre|Adrien M. Legendre]] 22: '''Legendre''' is a [[lunar]] impact [[crater]] that is locat... 24: The rim of Legendre is worn and eroded, with many small craterlets al... 28: ...e side of the crater mid-point that is closest to Legendre 32: !width="25%" style="background:#eeeeee;" |Legendre Legendre symbol (2478 bytes) 1: ...med after the French mathematician [[Adrien-Marie Legendre]]. 4: The Legendre symbol is a special case of the [[Jacobi symbol]]... 6: ...me number]] and ''a'' is an [[integer]], then the Legendre symbol <math>\left(\frac{a}{p}\right)</math> is: 11: ==Properties of the Legendre symbol== 12: There are a number of useful properties of the Legendre symbol which can be used to speed up calculations... Legendre transformation (10413 bytes) 1: ...ble]] functions ''f'' and ''g'' are said to be '''Legendre transforms''' of each other if their first [[deri... 5: ...re transformations are named after [[Adrien-Marie Legendre]]. They are unique up to an additive constant whi... 11: A Legendre transformation is its own inverse, and is related... 15: Legendre transformations are used in [[thermodynamics]] to... 19: ...ain (mathematics)|domain]]s of a function and its Legendre transform need not agree. Laguerre polynomials (1933 bytes) 1: In [[mathematics]], the '''Laguerre polynomials''', named after [[Edmond Laguerre]] (1834 - 1886)... 7: These polynomials are [[orthogonal polynomials|orthogonal]] to each other with respect to the [[... 29: These are also sometimes called '''Laguerre polynomials'''. They coincide with the definition given abov... 33: The sequence of Laguerre polynomials is a [[Sheffer sequence]]. 37: The Laguerre polynomials are defined in terms of [[confluent hypergeometri... Bell polynomials (2324 bytes) 1: ...rics|combinatorial]] [[mathematics]], the '''Bell polynomials''', named in honor of [[Eric Temple Bell]], are g... 48: The coefficients in these polynomials are the '''Faà di Bruno coefficients''', o... 60: * Eric Temple Bell, ''Partition Polynomials'', Annals of Mathematics, volume 29, 1927, pages ... Orthogonal polynomials (1463 bytes) 1: In [[mathematics]], two [[polynomials]] ''f'' and ''g'' are '''orthogonal''' to each ot... 5: ...eated as vectors and the [[inner product]] of two polynomials ''f''(''x'') and ''g''(''x'') is defined as 9: then the orthogonal polynomials are simply [[orthogonal]] vectors in this inner p... 11: ... ''n'', is said to be a sequence of '''orthogonal polynomials''' with respect to a "weight function" ''w'' when... 17: *The [[Hermite polynomials]] are orthogonal with respect to a [[normal distr... Fibonacci polynomials (702 bytes) 1: In [[mathematics]], '''Fibonacci polynomials''' are a generalization of [[Fibonacci number]]s.... 9: The first few Fibonacci polynomials are: 18: ...Fibonacci numbers are recovered by evaluating the polynomials at ''x'' = 1. Touchard polynomials (1582 bytes) 1: The '''Touchard polynomials''' comprise a [[polynomial sequence]] of [[binomi... 14: The Touchard polynomials make up the only polynomial sequence of binomial ... 16: The Touchard polynomials satisfy the recursion 22: The [[generating function]] of the Touchard polynomials is Hermite polynomials (6334 bytes) 1: In [[mathematics]], the '''Hermite polynomials,''' named in honor of [[Charles Hermite]] (pronou... 5: (the '''"probabilists' Hermite polynomials"'''), or sometimes by 9: (the '''"physicists' Hermite polynomials"'''). These two definitions are ''not'' exactly ... 17: The first several Hermite polynomials are: 29: ... 0, 1, 2, 3, .... These [[orthogonal polynomials|polynomials are orthogonal]] with respect to the [[measure]] Bernoulli polynomials (2771 bytes) 1: In [[mathematics]], the '''Bernoulli polynomials''' occur in the study of many [[special functions... 4: The generating function for the Bernoulli polynomials is 7: The generating function for the Euler polynomials is 16: The first few Bernoulli polynomials are: 25: The first few Euler polynomials are Chebyshev polynomials (7655 bytes) 1: ...re denoted ''T''<sub>''n''</sub> and '''Chebyshev polynomials of the second kind''' which are denoted ''U''<sub... 3: ...of degree ''n'' and the [[sequence]] of Chebyshev polynomials of either kind composes a [[polynomial sequence]]... 5: ...ation theory]] because the roots of the Chebyshev polynomials of the first kind, which are also called [[Chebys... 11: for the polynomials of the first and second kind, respectively. These... 14: The '''Chebyshev polynomials of the first kind''' are defined by the [[recurre... Calculus with polynomials (2095 bytes) 25: If one has polynomials with coefficients that are not real or complex nu... Gauss-Legendre algorithm (1589 bytes) 2: The '''Gauss-Legendre algorithm''' is an [[algorithm]] to compute the d... 4: ...riedrich Gauss]] (1777 - 1855) and [[Adrien-Marie Legendre]] (1752-1833) combined with modern algorithms for... Adrien-Marie Legendre (2437 bytes) 1: '''Adrien-Marie Legendre''' ([[September 18]] [[1752]]–[[January 10]... 3: ...mage:Adrien-Marie_Legendre.jpg|thumb|Adrien-Marie Legendre]] 5: ...in statistics and number theory completed that of Legendre. 11: Legendre did an impressive amount of work on elliptic func... 13: ...cs|theoretical mechanics]], he is known for the [[Legendre transform]], which is used to go from the Lagrang... Legendre's constant (816 bytes) 1: [[fr:Constante de Legendre]] 2: '''Legendre's constant''' is a "phantom" that doesn't really ... 4: ...e number|primes]] had led [[Adrien-Marie Legendre|Legendre]] to conjecture that perhaps 12: ...A''(''n'') turns out to be 1. Thus, there is no "Legendre's constant". 16: ...tp://mathworld.wolfram.com/LegendresConstant.html Legendre's constant] Legendre chi function (616 bytes) 1: In [[mathematics]], the '''Legendre chi function''' is defined as 7: The [[discrete fourier transform]] of the Legendre chi function with respect to the order ''n '' is ... 9: The Legendre chi function is a special case of the [[Lerch Tra... Polynomial sequence (657 bytes) 4: * [[Abel polynomials]] 5: * [[Bell polynomials]] 6: * [[Bernoulli polynomials]] 7: * [[Chebyshev polynomials]] 8: * [[Fibonacci polynomials]]
|
|||||
|
|
|
|
|
|
Copyright 2008 WordIQ.com - Privacy Policy
::
Terms of Use
:: Contact Us
:: About Us This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "legendre polynomials". |