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...

of the Legendre transformation which applies to non-convex functions. It is also known as Legendre–Fenchel transformation, Fenchel transformation, or Fenchel...

Hamilton's equations if the momentum is simultaneously changed by a Legendre transformation into P i = ∂ L ∂ Q ˙ i   , {\displaystyle P_{i}={\frac {\partial...

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

Associated Legendre polynomials Legendre's equation Legendre polynomials Legendre symbol Legendre transformation Legendre (crater), a lunar impact crater...

Legendre transformation Integral of inverse functions – Mathematical theorem, used in calculus Legendre transformation – Mathematical transformation Young's...

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

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

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

Convex metric space Convex optimization Duality Lagrange multiplier Legendre transformation Locally convex topological vector space Simplex Maps Convex conjugate...

canonical momenta). For a time instant t , {\displaystyle t,} the Legendre transformation of L {\displaystyle {\mathcal {L}}} is defined as the map ( q ...

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...

relation Legendre sieve Legendre symbol Legendre transformation Legendre transform (integral transform) Finite Legendre transform Legendre wavelet Legendre–Clebsch...

Whipple's transformation for Legendre functions, named after Francis John Welsh Whipple, arise from a general expression, concerning associated Legendre functions...

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

thermodynamic potential Helmholtz free energy (A = U - TS), a Legendre transformation of the energy. If, next to fluctuations of the energy, the macroscopic...

where C {\displaystyle C} is a constant. The left hand side is the Legendre transformation of L {\displaystyle L} with respect to f ′ ( x ) . {\displaystyle...

Functional Theory – Lecture Notes Density Functional Theory through Legendre Transformation Archived 2010-05-10 at the Wayback Machinepdf Burke, Kieron. "The...

(p1, p2, ..., pn) is an n-tuple of the generalized momenta. A Legendre transformation is performed to change the variables in the total differential...

integral Geodesic Isoperimetry Lagrangian Lagrangian mechanics Legendre transformation Luke's variational principle Minimal surface Morse theory Noether's...

involving their quadratic covariation. Integration by substitution Legendre transformation "Brook Taylor". History.MCS.St-Andrews.ac.uk. Retrieved May 25...

(digital image processing) Inverse scattering transform Legendre transformation Möbius transformation Perspective transform (computer graphics) Sequence transform...

The action S {\displaystyle S} in Hamilton's principle is the Legendre transformation of the action in Maupertuis' principle. The concepts and many of...

spatial and time coordinates, obtained from the Hamiltonian H via Legendre transformation. The initial and final conditions of the path integral are respectively...

resulting in the form (B, G, R): f(f(RGB)) = RGB, f(f(BGR)) = BGR. Legendre transformation, which converts between the Lagrangian and Hamiltonian, is an involutive...

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

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

Lagrangian formalism by a Legendre transformation, or from another set of canonical coordinates by a canonical transformation. Canonical coordinates are...

correlation functions. The quantum effective action is defined using the Legendre transformation of W [ J ] {\displaystyle W[J]} Γ [ ϕ ] = W [ J ϕ ] − ∫ d 4 x J...