mathematics, the Legendre forms of elliptic integrals are a canonical set of three elliptic integrals to which all others may be reduced. Legendre chose the...

In mathematics, Legendre polynomials, named after Adrien-Marie Legendre (1782), are a system of complete and orthogonal polynomials with a wide number...

They are a modern alternative to the Legendre forms. The Legendre forms may be expressed in terms of the Carlson forms and vice versa. The Carlson elliptic...

integral can be brought into a form that involves integrals over rational functions and the three Legendre canonical forms, also known as the elliptic integrals...

In numerical analysis, Gauss–Legendre quadrature is a form of Gaussian quadrature for approximating the definite integral of a function. For integrating...

In mathematics, the Legendre transformation (or Legendre transform), first introduced by Adrien-Marie Legendre in 1787 when studying the minimal surface...

In number theory, the Legendre symbol is a multiplicative function with values 1, −1, 0 that is a quadratic character modulo of an odd prime number p:...

filter Legendre form Legendre function Legendre moment Legendre polynomials Legendre pseudospectral method Legendre rational functions Legendre relation...

In mathematics, the associated Legendre polynomials are the canonical solutions of the general Legendre equation ( 1 − x 2 ) d 2 d x 2 P ℓ m ( x ) − 2...

In mathematics, Legendre's formula gives an expression for the exponent of the largest power of a prime p that divides the factorial n!. It is named after...

many applications. Alternate notations include: Carlson symmetric form Legendre form Nome Quarter period Elliptic functions: The inverses of elliptic integrals;...

In mathematics, Legendre's three-square theorem states that a natural number can be represented as the sum of three squares of integers n = x 2 + y 2 +...

supported wavelets derived from Legendre polynomials are termed Legendre wavelets or spherical harmonic wavelets. Legendre functions have widespread applications...

hyperbolic geometry. One proof of the Saccheri–Legendre theorem uses the Archimedean axiom, in the form that repeatedly halving one of two given angles...

calculation of any Legendre symbol, making it possible to determine whether there is an integer solution for any quadratic equation of the form x 2 ≡ a mod p...

polynomials of degree 2n − 1 or less. This exact rule is known as the Gauss–Legendre quadrature rule. The quadrature rule will only be an accurate approximation...

In mathematics, Legendre's relation can be expressed in either of two forms: as a relation between complete elliptic integrals, or as a relation between...

of the prime field of K, a finite field of order p2. Suppose E is in Legendre form, defined by the equation y 2 = x ( x − 1 ) ( x − λ ) {\displaystyle...

as ln(x) or loge(x). Legendre's constant is a mathematical constant occurring in a formula constructed by Adrien-Marie Legendre to approximate the behavior...

Legendre's conjecture, proposed by Adrien-Marie Legendre, states that there is a prime number between n 2 {\displaystyle n^{2}} and ( n + 1 ) 2 {\displaystyle...

^{2}(1-\lambda )^{2}}}\ .} which is the j-invariant of the elliptic curve of Legendre form y 2 = x ( x − 1 ) ( x − λ ) {\displaystyle y^{2}=x(x-1)(x-\lambda )}...

and foreshadowed the eventual development of infrastructure. In 1798, Legendre published Essai sur la théorie des nombres, which summarized the work of...

lemniscate arcsine and the lemniscate arccosine can also be expressed by the Legendre-Form: These functions can be displayed directly by using the incomplete elliptic...

Newtonian potential for a point mass. Just prior to that time, Adrien-Marie Legendre had investigated the expansion of the Newtonian potential in powers of...

nonlinear forms, depending on the relationship between the model parameters and the observed data. The method was first proposed by Adrien-Marie Legendre in...

(\nu +1)y=0} which can be put into Sturm–Liouville form, since ⁠d/dx⁠(1 − x2) = −2x, so the Legendre equation is equivalent to ( ( 1 − x 2 ) y ′ ) ′ +...

In mathematics, Legendre moments are a type of image moment and are achieved by using the Legendre polynomial. Legendre moments are used in areas of image...

process, then one obtains the Legendre polynomials. Another collection of orthogonal polynomials are the associated Legendre polynomials. The study of orthogonal...

depending on the application. 1 is the value of Legendre's constant, introduced in 1808 by Adrien-Marie Legendre to express the asymptotic behavior of the prime-counting...

}}\;\Gamma (2z).} It is also called the Legendre duplication formula or Legendre relation, in honor of Adrien-Marie Legendre. The multiplication theorem is Γ...