gives the complete elliptic integral of the first kind .
- Mathematical function, suitable for both symbolic and numerical manipulation.
- EllipticK is given in terms of the incomplete elliptic integral of the first kind by .
- EllipticK[m] has a branch cut discontinuity in the complex m plane running from to .
- For certain special arguments, EllipticK automatically evaluates to exact values.
- EllipticK can be evaluated to arbitrary numerical precision.
- EllipticK automatically threads over lists.
- EllipticK can be used with Interval and CenteredInterval objects. »
Examplesopen allclose all
Basic Examples (5)
Series expansion at Infinity:
Numerical Evaluation (5)
Specific Values (5)
Function Properties (9)
EllipticK is defined for all real values less than 1:
EllipticK takes all real positive values:
EllipticK is not an analytic function:
EllipticK is not a meromorphic function:
EllipticK is nondecreasing on its domain:
EllipticK is injective:
EllipticK is not surjective:
EllipticK is non-negative on its domain:
EllipticK is convex on its domain:
Indefinite integral of EllipticK:
Series Expansions (3)
Integral Transforms (3)
Plot the flow lines with bounds defined via EllipticK:
Compare with the result of EllipticFilterModel:
Properties & Relations (4)
Possible Issues (3)
Wolfram Research (1988), EllipticK, Wolfram Language function, https://reference.wolfram.com/language/ref/EllipticK.html (updated 2022).
Wolfram Language. 1988. "EllipticK." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2022. https://reference.wolfram.com/language/ref/EllipticK.html.
Wolfram Language. (1988). EllipticK. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/EllipticK.html