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For each s, this function gives an infinite sum, which takes some basic calculus to approach for even the simplest values of s. For example, if s=2, then 𝜁(s) is the well-known series 1 + 1/4 ...
This is a list of calculus topics. Limits. Limit (mathematics) Limit of a function. One-sided limit; Limit of a sequence; Indeterminate form; Orders of approximation
The energy of the vacuum is zero by definition, and assuming that all energy states can be thought of as particles in plane-waves, the mass gap is the mass of the lightest particle. For a given real field ϕ ( x ) {\displaystyle \phi (x)} , we can say that the theory has a mass gap if the two-point function has the property
This is a list of multivariable calculus topics. See also multivariable calculus, vector calculus, list of real analysis topics, list of calculus topics. Closed and exact differential forms; Contact (mathematics) Contour integral; Contour line; Critical point (mathematics) Curl (mathematics) Current (mathematics) Curvature; Curvilinear ...
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
At least in the mainstream media, the de facto 21st century analogue of Hilbert's problems is the list of seven Millennium Prize Problems chosen during 2000 by the Clay Mathematics Institute. Unlike the Hilbert problems, where the primary award was the admiration of Hilbert in particular and mathematicians in general, each prize problem ...
In calculus, the integral of a function is a generalization of area, mass, volume, sum, and total. The following pages list the integrals of many different functions. Lists of integrals; List of integrals of exponential functions; List of integrals of hyperbolic functions; List of integrals of inverse hyperbolic functions
Bolzano's theorem (real analysis, calculus) Bolzano–Weierstrass theorem (real analysis, calculus) Bombieri's theorem (number theory) Bombieri–Friedlander–Iwaniec theorem (number theory) Bondareva–Shapley theorem ; Bondy's theorem (graph theory, combinatorics) Bondy–Chvátal theorem (graph theory) Bonnet theorem (differential geometry)