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.

Legendre form (417 bytes)
1: In [[mathematics]], the '''Legendre forms of [[elliptic integral]]s''', ''F''(φ,'...

Associated Legendre polynomials (1240 bytes)
1: ...ndre polynomials]]''', named after [[Adrien-Marie Legendre]], are defined by:
5: These differ from the [[Legendre polynomials]].
13: ...ls]] of <math>\ \cos\theta</math>, the Associated Legendre polynomials are polynomials of <math>\cos\theta \...
15: The Associated Legendre polynomials are an important part of [[spherical ...
20: * [[Legendre polynomials]].

Legendre polynomials (4048 bytes)
1: ...times used (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: ...ions form a [[polynomial sequence]] called the '''Legendre polynomials'''.
11: Each Legendre polynomial P_''n''(''x'') is an ''n''th...

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'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]

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]]&ndash;[[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 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...

Jacobi symbol (2498 bytes)
4: The Jacobi symbol is a generalization of the [[Legendre symbol]] using the [[prime factorization]] of the...
10: #If ''n'' is prime, the Jacobi symbol is the Legendre symbol.
33: ...ic reciprocity|law of quadratic reciprocity]] for Legendre symbols.
36: ...nts about quadratic residuals with respect to the Legendre symbol cannot be made with the Jacobi symbol. Ho...
38: ...ct of Legendre symbols, there are cases where two Legendre symbols evaluate to &minus;1 and the Jacobi symbo...

Generalized Fourier series (3303 bytes)
21: == Example (Fourier-Legendre series) ==
22: The [[Legendre polynomials]] are solutions to the [[Sturm-Liouvi...
26: ...known as a Fourier-Legendre series) involving the Legendre polynomials, and
32: As an example, let us calculate the Fourier-Legendre series for ''f''(''x'')=cos ''x'' over [&minus;1,...
43: ...out 0. It may be advantageous to use such Fourier-Legendre series since the eigenfunctions are all polynomia...

Spherical harmonic (1367 bytes)
1: ...sed in terms of [[trigonometric function]]s and [[Legendre polynomials]]. This form comes from [[separation ...
7: where <math>P_\ell^m</math> are the [[associated Legendre polynomials]].
15: * [[Legendre polynomials]]

Robert Adrain (1807 bytes)
5: ...ble that he had read [[Adrien Marie Legendre|A.M. Legendre]]'s article on the topic (published 1804).
7: ...e physical measurements; in the case of Gauss and Legendre, the measurements in question were astronomical, ...

Christian Kramp (1673 bytes)
5: ...riedrich Bessel|Bessel]], [[Adrien-Marie Legendre|Legendre]] and [[Carl Friedrich Gauss|Gauss]] did, Kramp w...

Quadratic reciprocity (3710 bytes)
1: ...eonhard Euler|Euler]] and [[Adrien-Marie Legendre|Legendre]] and first satisfactorily proved by [[Karl Fried...
21: Using the [[Legendre symbol]]

Palitzsch (crater) (1713 bytes)
22: ...hile to the east-southeast is [[Legendre (crater)|Legendre crater]].

Adams (Lunar crater) (2018 bytes)
9: ... just to the southwest of the [[Legendre (crater)|Legendre crater]]. To the northwest are the [[Hase (crater...

Polynomial sequence (657 bytes)
10: * [[Legendre polynomials]]

GNU Scientific Library (5471 bytes)
41: *** [[Definition of Legendre form]]s
43: *** [[Legendre form of complete elliptic integral]]s
44: *** [[Legendre form of incomplete elliptic integral]]s
71: ** [[Legendre functions and spherical harmonic]]s
72: *** [[Legendre polynomial]]s

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