Weierstrass elliptic functions
GPTKB entity
Statements (28)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
elliptic function
|
| gptkbp:category |
special functions
|
| gptkbp:definedIn |
gptkb:complex_plane
|
| gptkbp:differential |
(℘')^2 = 4℘^3 - g2℘ - g3
|
| gptkbp:field |
gptkb:mathematics
complex analysis |
| gptkbp:firstPublished |
1862
|
| gptkbp:generalizes |
trigonometric functions
|
| gptkbp:hasAdditionTheorem |
yes
|
| gptkbp:hasLaurentExpansion |
at origin
|
| gptkbp:hasPole |
order 2
|
| gptkbp:hasSeriesExpansion |
gptkb:Laurent_series
|
| https://www.w3.org/2000/01/rdf-schema#label |
Weierstrass elliptic functions
|
| gptkbp:inverseFunction |
gptkb:integral
|
| gptkbp:namedAfter |
gptkb:Karl_Weierstrass
|
| gptkbp:notation |
℘ (Weierstrass P)
|
| gptkbp:parameter |
g2
g3 |
| gptkbp:period |
doubly periodic
|
| gptkbp:relatedTo |
Jacobi elliptic functions
modular forms elliptic curves |
| gptkbp:satisfies |
partial differential equations
|
| gptkbp:usedIn |
gptkb:algebraic_geometry
number theory theory of elliptic integrals |
| gptkbp:bfsParent |
gptkb:Karl_Weierstrass
|
| gptkbp:bfsLayer |
5
|