- mathematics, the
Liouvillian functions comprise a set of
functions including the
elementary functions and
their repeated integrals.
Liouvillian functions can...
- t}}=\{\,H,\rho \,\}} or, in
terms of the
linear Liouville operator or
Liouvillian, i L ^ = ∑ i = 1 n [ ∂ H ∂ p i ∂ ∂ q i − ∂ H ∂ q i ∂ ∂ p i ] = − { H...
- "closed-form number"; in
increasing order of generality,
these are the
Liouvillian numbers (not to be
confused with
Liouville numbers in the
sense of rational...
-
nonelementary integral. The
Liouvillian functions are
defined as the
elementary functions and, recursively, the
integrals of the
Liouvillian functions. The mathematical...
-
equation y′ = By.) An
extension F ⊆ K of
differential fields is
called Liouvillian if all
constants are in F, and K can be
generated by
adjoining a finite...
- In
number theory, a
Liouville number is a real
number x {\displaystyle x} with the
property that, for
every positive integer n {\displaystyle n} , there...
-
Sudarshan and Göran Lindblad),
master equation in
Lindblad form,
quantum Liouvillian, or
Lindbladian is one of the
general forms of
Markovian master equations...
-
integration of the set of the
elementary functions is the set of the
Liouvillian functions.
Algebraic function –
Mathematical function Closed-form expression –...
- {\displaystyle W}
function cannot be
expressed in
terms of
elementary (
Liouvillian) functions, the
first published proof did not
appear until 2008. There...
- {\displaystyle i{\hat {L}}=-\{H,\cdot \}} , is
sometimes referred to as the
Liouvillian (see Liouville's
theorem (Hamiltonian)). The
concept of
Poisson brackets...
