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Aide de Scilab >> Fonctions spéciales > %k

%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)]}

Reference : Abramowitz and Stegun page 598

Examples

m = 0.4;
[%k(m) delip(1, sqrt(m))]
%k([-%inf -10 -1 0 0.1 0.3 0.9])
%k(0)==%pi/2
--> 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

  • delip — intégrale elliptique complete ou incomplete du premier type
  • ellipj — Jacobi elliptic functions
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Last updated:
Tue Feb 25 08:50:24 CET 2020