Incomplete elliptic integral of the first kind
GPTKB entity
Statements (27)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:defines |
F(φ, k) = ∫₀^φ (1 / sqrt(1 - k^2 sin^2 θ)) dθ
|
| gptkbp:field |
gptkb:mathematics
gptkb:elliptic_integrals analysis |
| gptkbp:hasSpecialCase |
complete elliptic integral of the first kind
|
| https://www.w3.org/2000/01/rdf-schema#label |
Incomplete elliptic integral of the first kind
|
| gptkbp:notation |
F(φ, k)
F(φ | k) F(φ, m) |
| gptkbp:parameter |
amplitude φ
modulus k |
| gptkbp:property |
multivalued function
analytic function of φ and k can be expressed as a power series reduces to elementary functions for k=0 reduces to elementary functions for φ=0 |
| gptkbp:relatedTo |
Jacobi elliptic functions
|
| gptkbp:seeAlso |
gptkb:Carl_Gustav_Jacobi
gptkb:Legendre_form Elliptic integral |
| gptkbp:usedIn |
gptkb:geometry
engineering physics calculation of arc length of ellipse |
| gptkbp:bfsParent |
gptkb:Elliptic_Integrals
|
| gptkbp:bfsLayer |
8
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