Complete elliptic integral of the first kind
GPTKB entity
Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:software
|
| gptkbp:alsoKnownAs |
K(k)
|
| gptkbp:appearsIn |
theory of elliptic functions
calculation of arc length of ellipse |
| gptkbp:definedIn |
K(k) = ∫₀^{π/2} (1 - k^2 sin^2 θ)^{-1/2} dθ
|
| gptkbp:dependsOn |
modulus k
|
| gptkbp:divergesAt |
k = 1
|
| gptkbp:domain |
0 ≤ k < 1
|
| gptkbp:hasInverse |
Jacobi amplitude function
|
| gptkbp:hasSeriesExpansion |
K(k) = (π/2) Σ_{n=0}^∞ [(2n)!/(2^n n!)^2] k^{2n}
|
| https://www.w3.org/2000/01/rdf-schema#label |
Complete elliptic integral of the first kind
|
| gptkbp:isEvenFunction |
k
|
| gptkbp:namedAfter |
gptkb:Carl_Gustav_Jacobi
|
| gptkbp:notation |
K(k)
K(m), where m = k^2 |
| gptkbp:relatedTo |
gptkb:elliptic_integrals
incomplete elliptic integral of the first kind |
| gptkbp:specialValueAt |
K(0) = π/2
|
| gptkbp:usedIn |
engineering
mathematical analysis physics |
| gptkbp:bfsParent |
gptkb:Elliptic_Integrals
|
| gptkbp:bfsLayer |
8
|