Statements (51)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:application |
cryptography
mathematical physics number theory calculation of arc length of ellipse electrostatics of ellipsoids geodesics on ellipsoids magnetic field of coils solving Kepler's equation solving pendulum equations |
| gptkbp:category |
gptkb:software
|
| gptkbp:designer |
elliptic functions
|
| gptkbp:field |
gptkb:mathematics
|
| gptkbp:generalizes |
inverse trigonometric functions
|
| gptkbp:hasProperty |
multivalued
not elementary can be expressed in terms of hypergeometric functions |
| gptkbp:hasSubfield |
analysis
calculus complex analysis |
| gptkbp:hasType |
complete elliptic integral
elliptic integral of the first kind elliptic integral of the second kind elliptic integral of the third kind incomplete elliptic integral |
| gptkbp:historically_studiedBy |
gptkb:Carl_Gustav_Jacobi
gptkb:Niels_Henrik_Abel gptkb:Adrien-Marie_Legendre |
| https://www.w3.org/2000/01/rdf-schema#label |
elliptic integrals
|
| gptkbp:notation |
E(φ, k)
F(φ, k) Π(n; φ, k) |
| gptkbp:originatedIn |
gptkb:gravitational_potential
electrostatics arc length of ellipse pendulum motion magnetic field calculations integrals of rational functions with square roots of polynomials of degree 3 or 4 |
| gptkbp:relatedTo |
elliptic functions
modular forms theta functions |
| gptkbp:tabulatedBy |
gptkb:Jacobi
gptkb:Legendre |
| gptkbp:usedIn |
gptkb:astronomy
gptkb:geometry electromagnetism engineering mechanics physics |
| gptkbp:bfsParent |
gptkb:Abelian_integrals
|
| gptkbp:bfsLayer |
7
|