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Nonelementary integral. In mathematics, a nonelementary antiderivative of a given elementary function is an antiderivative (or indefinite integral) that is, itself, not an elementary function (i.e. a function constructed from a finite number of quotients of constant, algebraic, exponential, trigonometric, and logarithmic functions using field ...
Advanced. Specialized. Miscellaneous. v. t. e. In calculus, symbolic integration is the problem of finding a formula for the antiderivative, or indefinite integral, of a given function f (x), i.e. to find a formula for a differentiable function F (x) such that. This is also denoted.
In mathematics, Liouville's theorem, originally formulated by French mathematician Joseph Liouville in 1833 to 1841, [1][2][3] places an important restriction on antiderivatives that can be expressed as elementary functions. The antiderivatives of certain elementary functions cannot themselves be expressed as elementary functions.
Nonlinear dynamics. Game theory. v. t. e. In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. [1][2] Nonlinear problems are of interest to engineers, biologists, [3][4][5] physicists, [6][7] mathematicians, and many other scientists ...
Sokhotski–Plemelj theorem. The Sokhotski–Plemelj theorem (Polish spelling is Sochocki) is a theorem in complex analysis, which helps in evaluating certain integrals. The real-line version of it (see below) is often used in physics, although rarely referred to by name. The theorem is named after Julian Sochocki, who proved it in 1868, and ...
More detail may be found on the following pages for the lists of integrals: Gradshteyn, Ryzhik, Geronimus, Tseytlin, Jeffrey, Zwillinger, and Moll 's (GR) Table of Integrals, Series, and Products contains a large collection of results. An even larger, multivolume table is the Integrals and Series by Prudnikov, Brychkov, and Marichev (with ...
Integrable system. In mathematics, integrability is a property of certain dynamical systems. While there are several distinct formal definitions, informally speaking, an integrable system is a dynamical system with sufficiently many conserved quantities, or first integrals, that its motion is confined to a submanifold of much smaller ...
Common integrals in quantum field theory. Common integrals in quantum field theory are all variations and generalizations of Gaussian integrals to the complex plane and to multiple dimensions. [1]: 13–15 Other integrals can be approximated by versions of the Gaussian integral. Fourier integrals are also considered.