List of topics named after Karl Weierstrass
Encyclopedia
Named after Weierstrass and other persons
- Bolzano–Weierstrass theoremBolzano–Weierstrass theoremIn real analysis, the Bolzano–Weierstrass theorem is a fundamental result about convergence in a finite-dimensional Euclidean space Rn. The theorem states thateach bounded sequence in Rn has a convergent subsequence...
- Casorati–Weierstrass theorem
- Durand–Kerner method, also called the method of Weierstrass
- Enneper–Weierstrass parameterization
- Lindemann–Weierstrass theoremLindemann–Weierstrass theoremIn mathematics, the Lindemann–Weierstrass theorem is a result that is very useful in establishing the transcendence of numbers. It states that if 1, ..., are algebraic numbers which are linearly independent over the rational numbers ', then 1, ..., are algebraically...
- Sokhatsky–Weierstrass theorem
- Stone–Weierstrass theorem
- Weierstrass–Casorati theorem – see Casorati–Weierstrass theorem
- Weierstrass–Enneper parameterization
- Weierstrass–Erdmann conditionWeierstrass–Erdmann conditionThe Weierstrass–Erdmann condition is a technical tool from the calculus of variations. This condition gives the sufficient conditions for an extremal to have a corner.- Conditions :...
Named after Weierstrass alone
- Weierstrass approximation theorem
- Weierstrass's elliptic functionsWeierstrass's elliptic functionsIn mathematics, Weierstrass's elliptic functions are elliptic functions that take a particularly simple form; they are named for Karl Weierstrass...
- Weierstrass factorization theoremWeierstrass factorization theoremIn mathematics, the Weierstrass factorization theorem in complex analysis, named after Karl Weierstrass, asserts that entire functions can be represented by a product involving their zeroes...
- Weierstrass functionWeierstrass functionIn mathematics, the Weierstrass function is a pathological example of a real-valued function on the real line. The function has the property that it is continuous everywhere but differentiable nowhere...
- Weierstrass M-test
- Weierstrass pointWeierstrass pointIn mathematics, a Weierstrass point P on a nonsingular algebraic curve C defined over the complex numbers is a point such that there are extra functions on C, with their poles restricted to P only, than would be predicted by looking at the Riemann–Roch theorem...
- Weierstrass preparation theoremWeierstrass preparation theoremIn mathematics, the Weierstrass preparation theorem is a tool for dealing with analytic functions of several complex variables, at a given point P...
- Weierstrass product inequalityWeierstrass product inequalityIn mathematics, the Weierstrass product inequality states that given real numbers 0 ≤ a, b, c, d ≤ 1, it follows that+a+b+c+d \geq 1. \,...
- Weierstrass ringWeierstrass ringIn mathematics, a Weierstrass ring, named by after Karl Weierstrass, is a commutative local ring that is Henselian, pseudo-geometric, and such that any quotient ring by a prime ideal is a finite extension of a regular local ring.-Examples:...
- Weierstrass substitutionWeierstrass substitutionIn integral calculus, the Weierstrass substitution, named after Karl Weierstrass, is used for finding antiderivatives, and hence definite integrals, of rational functions of trigonometric functions. No generality is lost by taking these to be rational functions of the sine and cosine. The...
- Weierstrass theoremWeierstrass theoremSeveral theorems are named after Karl Weierstrass. These include:*The Weierstrass approximation theorem, of which one well known generalization is the Stone–Weierstrass theorem...
– any of several theorems - Weierstrass transformWeierstrass transformIn mathematics, the Weierstrass transform of a function f : R → R, named after Karl Weierstrass, is the function F defined by...
Typography
- Weierstrass pWeierstrass pIn mathematics, the Weierstrass p , also called pe, is used for the Weierstrass's elliptic function. It is occasionally used for the power set, although for that purpose a cursive capital, rather than lower-case, p is more widespread...
, a form of the letter p used to denote the Weierstrass elliptic function