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

mathematics. Well-known and important concepts such as the Legendre polynomials and Legendre transformation are named after him. He is also known for his contributions...

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

systems evolving in time. The De Donder–Weyl theory is based on a change of variables known as Legendre transformation. Let xi be spacetime coordinates...

change of thermodynamic potential is equivalent to a Legendre transformation, and Legendre transformations do not act in the equilibrium space, it is necessary...

aims of studying differential equations (e.g. the Legendre transformation or canonical transformation) and describing the 'change of space element', familiar...

underlie the Hamiltonian and Lagrangian formulations, and the Legendre transformation that connects them. Among his notable contributions are the Tulczyjew...

In mathematics, a transformation of a sequence's generating function provides a method of converting the generating function for one sequence into a generating...

et sur la comparaison de ces arcs. In: Histoire de l’Académie royale des sciences Paris (1788), S. 644–683. Adrien-Marie Legendre: Mémoire sur les transcendantes...

and the three Legendre canonical forms, also known as the elliptic integrals of the first, second and third kind. Besides the Legendre form given below...

Rodrigues' rotation formula for vectors, the Rodrigues formula for the Legendre polynomials, and the Euler–Rodrigues parameters. Rodrigues was born into...

These include most of the commonly used functions of mathematical physics. Legendre functions are solutions of a second order differential equation with 3...

equation Legendre transformation Clairaut 1734. Kamke 1944. Clairaut, Alexis Claude (1734), "Solution de plusieurs problèmes où il s'agit de trouver des...

time in the evening, Louis Legendre was sent out with troops to arrest leading members of the Montagnards at the Hôtel de Ville and the Jacobin Club itself...

which w = f(z) is a constant. The linear fractional transformation, also known as a Möbius transformation, has many fascinating properties. Four of these...

R_{k}\cdot \varphi +J\cdot \varphi \right)} where J is the source field. The Legendre transform of Wk ordinarily gives the effective action. However, the action...

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...

1.2 (pages 2–3) and Chapter 3. de Berg et al. (2008), p. 254. Grünbaum (2003), p. 57. de Berg et al. (2008), p. 256. de Berg et al. (2008), p. 245. Rappoport...

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

momenta in phase space). Both formulations are equivalent by a Legendre transformation on the generalized coordinates, velocities and momenta; therefore...

quadrature Gauss–Kronrod quadrature formula Gauss–Newton algorithm Gauss–Legendre algorithm Gauss's complex multiplication algorithm Gauss's theorem may...

subject of free probability. A free entropy is generated by a Legendre transformation of the entropy. The different potentials correspond to different...

momenta in phase space. Both formulations are equivalent by a Legendre transformation on the generalized coordinates, velocities and momenta; therefore...

triangle is larger than either of the remote angles), as well as the Saccheri–Legendre theorem, which states that the sum of the measures of the angles in a triangle...

widespread standardized method to identify indicator plants. Dufrene, Marc; Legendre, Pierre (August 1997). "Species Assemblages and Indicator Species: The...

Lagrangian stage, before passing over to Hamiltonian mechanics via the Legendre transformation. The Hamiltonian density is related to the Lie derivative of the...

Mackie, Meaghan; Sakalauskaite, Jorune; Stiller, Josefin; Clarke, Julia A.; Legendre, Lucas J.; Douglass, Kristina; Hansford, James; Haile, James; Bunce, Michael...

connection to this, he also introduced the Christoffel–Darboux formula for Legendre polynomials (he later also published the formula for general orthogonal...

L}{\partial {\dot {q}}_{i}}}-L} and can be obtained by performing a Legendre transformation on the Lagrangian, which introduces new variables canonically conjugate...

of a thermodynamic system. Conjugate setups are associated by Legendre transformations. The ratio of two extensive properties of the same object or system...