Statements (21)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:category |
real analysis
counterexample in mathematics |
| gptkbp:example |
pathological function
|
| gptkbp:field |
mathematical analysis
|
| gptkbp:form |
W(x) = \\sum_{n=0}^{\\infty} a^n \\cos(b^n \\pi x)
|
| https://www.w3.org/2000/01/rdf-schema#label |
Weierstrass function
|
| gptkbp:influenced |
development of fractal geometry
|
| gptkbp:introducedIn |
1872
|
| gptkbp:namedAfter |
gptkb:Karl_Weierstrass
|
| gptkbp:parameterCondition |
0 < a < 1
ab > 1 + 3\\pi/2 b is a positive odd integer |
| gptkbp:property |
continuous everywhere
nowhere differentiable |
| gptkbp:relatedTo |
gptkb:Takagi_function
Brownian motion fractal nowhere differentiable function |
| gptkbp:bfsParent |
gptkb:Karl_Weierstrass
|
| gptkbp:bfsLayer |
5
|