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1. Integrals in involution: Solutions of differential equations whose Jacobi brackets vanish identically. A function $G(x,u,p)$ of $2n+1$ variables $x=(x_1,\dots,x_n)$, $u$, $p=(p_1,\dots,p_n)$ is a first integral of the first-order partial differential equation $$F ... (Mathematics) [100%] 2023-08-27
2. Table of Indefinite Integrals: This is a table of common antiderivatives and definite integrals for the Calculus students. Remember after each indefinite integral there is a general constant of integration (+C). [86%] 2023-02-26 [Mathematics] [Calculus]...
3. Euler integrals: The integral $$ B(p,q) = \int_0^1 x^{p-1}(1-x)^{q-1}\rd x, \quad p,q > 0, $$ called the Euler integral of the first kind, or the beta-function, and $$ \int_0^\infty x^{s-1}e^{-x ... (Mathematics) [100%] 2023-12-19
4. Slater integrals: In mathematics and mathematical physics, Slater integrals are certain integrals of products of three spherical harmonics. They occur naturally when applying an orthonormal basis of functions on the unit sphere that transform in a particular way under rotations in three ... (Physics) [100%] 2023-11-01 [Atomic physics] [Quantum chemistry]...
5. Fresnel integrals: The special functions $$ C ( x) = { \frac{1}{\sqrt {2 \pi } } } \int\limits _ { 0 } ^ { {x ^ {2}} } \frac{\cos t }{\sqrt t } dt = \ \sqrt { \frac{2} \pi } \int\limits _ { 0 } ^ { x } \cos t ^ {2} dt, $$ $$ S ( x) = { \frac{1}{\sqrt ... (Mathematics) [100%] 2023-11-04
6. Wallis integrals: In mathematics, and more precisely in analysis, the Wallis integrals constitute a family of integrals introduced by John Wallis. The Wallis integrals are the terms of the sequence \displaystyle{ (W_n)_{n \geq 0} }[/math] defined by or equivalently, The ... (Family of mathematical integrals) [100%] 2024-08-05 [Integrals]
7. Lists of integrals: Integration is the basic operation in integral calculus. While differentiation has straightforward rules by which the derivative of a complicated function can be found by differentiating its simpler component functions, integration does not, so tables of known integrals are often ... (None) [81%] 2023-12-15 [Lists of integrals] [Mathematical identities]...
8. Multiloop Feynman integrals: Multiloop Feynman integrals appear when quantum-field amplitudes are constructed within perturbation theory. They are integrals over so-called loop momenta. [81%] 2021-12-24 [Physics] [Quantum and Statistical Field Theory]...
9. Differentiation of integrals: In mathematics, the problem of differentiation of integrals is that of determining under what circumstances the mean value integral of a suitable function on a small neighbourhood of a point approximates the value of the function at that point. More ... [81%] 2023-12-11 [Differentiation rules] [Measure theory]...
10. Applying definite integrals: For a discussion on the basic theory of integrals see: w:Riemann sum Imagine an object O {\displaystyle {\mathcal {O}}} that is free to move in one dimension — say, along the x {\displaystyle x} axis. Like every physical object, it ... [81%] 2023-03-21 [Calculus] [Definite integrals]...
11. Differentiation of integrals: In mathematics, the problem of differentiation of integrals is that of determining under what circumstances the mean value integral of a suitable function on a small neighbourhood of a point approximates the value of the function at that point. More ... (Problem in mathematics) [81%] 2024-12-10 [Differentiation rules] [Measure theory]...
12. Time evolution of integrals: Within differential calculus, in many applications, one needs to calculate the rate of change of a volume or surface integral whose domain of integration, as well as the integrand, are functions of a particular parameter. In physical applications, that parameter ... (Change of time of the value of an integral) [70%] 2023-02-26 [Differential calculus] [Integral calculus]...
13. List of definite integrals: In mathematics, the definite integral is the area of the region in the xy-plane bounded by the graph of f, the x-axis, and the lines x = a and x = b, such that area above the x-axis adds ... (none) [70%] 2023-07-17 [Integrals] [Mathematics-related lists]...
14. Feynman path integrals for mathematicians: Feynman path integral, or simply path integral, is a gadget whereby physicists calculate probability amplitudes for quantum transitions by "summing over all possible classical histories (or paths)". Naively, it makes no sense, but it is powerful and aesthetically pleasing. [63%] 2023-12-12 [Mathematics]
15. Path integrals in polymer science: A polymer is a macromolecule, composed of many similar or identical repeated subunits. Polymers are common in, but not limited to, organic media. [63%] 2023-12-03 [Condensed matter physics] [Polymers]...
16. Fatou theorem (on Lebesgue integrals): A theorem on passing to the limit under a Lebesgue integral: If a sequence of measurable (real-valued) non-negative functions $ f _ {1} , f _ {2} \dots $ converges almost-everywhere on a set $ E $ to a function $ f $, then ... (Mathematics) [63%] 2023-09-15
17. Path integrals in polymer science: A polymer is a macromolecule, composed of many similar or identical repeated subunits. Polymers are common in, but not limited to, organic media. (Physics) [63%] 2022-09-01 [Condensed matter physics] [Polymers]...
18. List of integrals of rational functions: The following is a list of integrals (antiderivative functions) of rational functions. Any rational function can be integrated by partial fraction decomposition of the function into a sum of functions of the form: which can then be integrated term by ... (None) [57%] 2023-02-15 [Lists of integrals]
19. 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. Other integrals can be approximated by versions of the Gaussian integral. (Physics) [57%] 2023-02-09 [Quantum field theory] [Mathematical physics]...
20. List of integrals of irrational functions: The following is a list of integrals (antiderivative functions) of irrational functions. For a complete list of integral functions, see lists of integrals. (none) [57%] 2023-02-15 [Lists of integrals]
21. List of integrals of logarithmic functions: The following is a list of integrals (antiderivative functions) of logarithmic functions. For a complete list of integral functions, see list of integrals. (none) [57%] 2024-01-08 [Lists of integrals]
22. List of integrals of logarithmic functions: The following is a list of integrals (antiderivative functions) of logarithmic functions. For a complete list of integral functions, see list of integrals. (none) [57%] 2023-12-01 [Lists of integrals]
23. List of integrals of hyperbolic functions: The following is a list of integrals (anti-derivative functions) of hyperbolic functions. For a complete list of integral functions, see list of integrals. (none) [57%] 2023-03-10 [Exponentials] [Lists of integrals]...
24. List of integrals of irrational functions: The following is a list of integrals (antiderivative functions) of irrational functions. For a complete list of integral functions, see lists of integrals. (none) [57%] 2023-11-06 [Lists of integrals]
25. List of integrals of trigonometric functions: The following is a list of integrals (antiderivative functions) of trigonometric functions. For antiderivatives involving both exponential and trigonometric functions, see List of integrals of exponential functions. (None) [57%] 2024-07-28 [Lists of integrals] [Trigonometry]...
26. List of integrals of Gaussian functions: In the expressions in this article, \displaystyle{ \phi(x) = \frac{1}{\sqrt{2\pi}}e^{-\frac{1}{2} x^2} }[/math] is the standard normal probability density function, \displaystyle{ \Phi(x) = \int_{-\infty}^x \phi(t) \, dt = \frac{1}{2 ... (none) [57%] 2024-08-05 [Lists of integrals] [Gaussian function]...
27. List of integrals of hyperbolic functions: The following is a list of integrals (anti-derivative functions) of hyperbolic functions. For a complete list of integral functions, see list of integrals. (Wikipedia list article) [57%] 2024-08-06 [Exponentials] [Lists of integrals]...
28. List of integrals of exponential functions: The following is a list of integrals of exponential functions. For a complete list of integral functions, please see the list of integrals. (List Of Integrals Of Exponential Functions) [57%] 2024-08-07 [Exponentials] [Lists of integrals]...
29. List of integrals of trigonometric functions: The following is a list of integrals (antiderivative functions) of trigonometric functions. For antiderivatives involving both exponential and trigonometric functions, see List of integrals of exponential functions. (None) [57%] 2024-08-07 [Lists of integrals] [Trigonometry]...
30. List of integrals of inverse trigonometric functions: The following is a list of indefinite integrals (antiderivatives) of expressions involving the inverse trigonometric functions. For a complete list of integral formulas, see lists of integrals. (Wikipedia list article) [53%] 2023-02-15 [Lists of integrals]