Complete elliptic integral of the third kind
GPTKB entity
Statements (22)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:software
|
| gptkbp:alsoKnownAs |
Π(n, k)
|
| gptkbp:application |
elliptic functions
engineering physics |
| gptkbp:category |
gptkb:integral
gptkb:software |
| gptkbp:defines |
Π(n, k) = ∫₀^{π/2} (1 / (1 - n sin²θ)) (dθ / sqrt(1 - k² sin²θ))
|
| gptkbp:field |
gptkb:mathematics
mathematical analysis |
| https://www.w3.org/2000/01/rdf-schema#label |
Complete elliptic integral of the third kind
|
| gptkbp:notation |
Π(n | k)
Π(n, k) |
| gptkbp:property |
reduces to complete elliptic integral of the second kind when n = k^2
reduces to complete elliptic integral of the first kind when n = 0 |
| gptkbp:relatedTo |
gptkb:integral
complete elliptic integral of the first kind complete elliptic integral of the second kind |
| gptkbp:variant |
k (modulus)
n (characteristic) |
| gptkbp:bfsParent |
gptkb:Elliptic_Integrals
|
| gptkbp:bfsLayer |
8
|