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Scilabヘルプ >> Special Functions > %k

%k

ヤコビの完全楕円積分

呼び出し手順

K = %k(m)

パラメータ

m

vector of real numbers in (-∞,1): 楕円積分パラメーター

K

vector of respective values of the integral.

説明

ヤコビの第一種完全楕円積分を計算します :

K(m) = integral_0^1 {dt / sqrt[(1 - t^2)(1 - m.t^2)]}

参考文献 : Abramowitz and Stegun page 598

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

参照

  • delip — 第一種の完全および不完全楕円積分
  • ellipj — Jacobi elliptic functions
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Last updated:
Tue Feb 25 08:53:21 CET 2020