Complete elliptic integral of the second kind
GPTKB entity
Statements (25)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:software
|
| gptkbp:alsoKnownAs |
E(k)
|
| gptkbp:appearsIn |
arc length of ellipse
|
| gptkbp:definedIn |
E(k) = ∫₀^{π/2} sqrt(1 - k^2 sin^2 θ) dθ
|
| gptkbp:dependsOn |
modulus k
|
| gptkbp:hasAsymptoticExpansion |
E(k) ≈ 1 + (1/2)ln(4/(1-k)) as k→1⁻
|
| gptkbp:hasSeriesExpansion |
E(k) = (π/2) [1 - (1/4)k^2 - (3/64)k^4 - (5/256)k^6 - ...]
|
| gptkbp:hasSpecialCase |
E(0) = π/2
E(1) = 1 |
| https://www.w3.org/2000/01/rdf-schema#label |
Complete elliptic integral of the second kind
|
| gptkbp:implementedIn |
gptkb:Mathematica
gptkb:Matlab Python (scipy.special.ellipe) |
| gptkbp:isEvenFunctionOf |
k
|
| gptkbp:isRealFor |
0 ≤ k ≤ 1
|
| gptkbp:isTabulatedIn |
mathematical tables
|
| gptkbp:parameter |
modulus k
parameter m = k^2 |
| gptkbp:relatedTo |
gptkb:elliptic_integrals
complete elliptic integral of the first kind |
| gptkbp:usedIn |
engineering
mathematical analysis physics |
| gptkbp:bfsParent |
gptkb:Elliptic_Integrals
|
| gptkbp:bfsLayer |
8
|