%k
Jacobi's complete elliptic integral of the first kind (vectorized)
Syntax
K = %k(m)
Arguments
- m
vector of real numbers in [-∞,1): parameter of the elliptic integral.
- K
vector of respective values of the integral.
Description
Computes and provides values of the Jacobi's complete elliptic integral of the first kind, defined as
![K(m) = integral_0^1 {dt / sqrt[(1 - t^2)(1 - m.t^2)]}](/docs/2025.0.0/fr_FR/_LaTeX_percentk.xml_1.png)
Reference : Abramowitz and Stegun page 598
Examples
--> m = 0.4; --> [%k(m) delip(1, sqrt(m))] ans = 1.7775194 1.7775194 --> %k([-%inf -10 -1 0 0.1 0.3 0.9]) ans = 0. 0.7908719 1.3110288 1.5707963 1.6124413 1.7138894 2.5780921 --> %k(0)==%pi/2 ans = T
See also
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