rtoy
commented
3 months ago Imported from SourceForge on 2024-07-05 22:36:20 Created by robert_dodier on 2016-09-16 05:24:28 Original: https://sourceforge.net/p/maxima/bugs/3214/#1f36
- Description has changed:
Diff:
--- old
+++ new
@@ -2,15 +2,17 @@
Given the following input:
-> q(x, y) := exp(-%pi * elliptic_kc( ( 1 - x^y )^(1/y) ) / elliptic_kc(x))$
-> Theta[2](x, y, n) := 2 * y^0.25 * sum( y^(k * (k + 1)) * cos((2 * k + 1) * x), k, 0, n );
-> Theta[3](x, y, n) := 1 + 2 * sum( y^(k^2) * cos(2 * k * x), k, 1, n );
-> [_u, _m, N] : [25, 0.999999, 5]$
-> U(x, y) := %pi * x / (2 * elliptic_kc(y))$
-> M(y) := q(y, 1)$
-> float(Theta[2](U(_u, _m), M(_m), N) / Theta[3](U(_u, _m), M(_m), N) / _m^0.25);
-> jacobi_cd(_u, _m);
-> wxplot2d([Theta[2](U(x, _m), M(_m), N) / Theta[3](U(x, _m), M(_m), N) / _m^0.25 - jacobi_cd(x + 0*elliptic_kc(_m), _m)],
-> [x, 0, 4*elliptic_kc(_m)])$
+~~~~
+q(x, y) := exp(-%pi * elliptic_kc( ( 1 - x^y )^(1/y) ) / elliptic_kc(x))$
+Theta[2](x, y, n) := 2 * y^0.25 * sum( y^(k * (k + 1)) * cos((2 * k + 1) * x), k, 0, n );
+Theta[3](x, y, n) := 1 + 2 * sum( y^(k^2) * cos(2 * k * x), k, 1, n );
+[_u, _m, N] : [25, 0.999999, 5]$
+U(x, y) := %pi * x / (2 * elliptic_kc(y))$
+M(y) := q(y, 1)$
+float(Theta[2](U(_u, _m), M(_m), N) / Theta[3](U(_u, _m), M(_m), N) / _m^0.25);
+jacobi_cd(_u, _m);
+plot2d([Theta[2](U(x, _m), M(_m), N) / Theta[3](U(x, _m), M(_m), N) / _m^0.25 - jacobi_cd(x + 0*elliptic_kc(_m), _m)],
+ [x, 0, 4*elliptic_kc(_m)])$
+~~~~
-I ran into some strange results when trying to approximate jacobi_cd() with theta functions. The errors are hinted as early as _m=0.9, and get bigger from there on. Using jacobi_sn( u + elliptic_kc(m), m ) the results are correct. It's true it's extremely unlikely (I'd say impossible) to get to such a modulus in my quests, but I thought I'd let you know.
+I ran into some strange results when trying to approximate jacobi_cd() with theta functions. The errors are hinted as early as `_m=0.9`, and get bigger from there on. Using jacobi_sn( u + elliptic_kc(m), m ) the results are correct. It's true it's extremely unlikely (I'd say impossible) to get to such a modulus in my quests, but I thought I'd let you know.
Imported from SourceForge on 2024-07-05 22:36:19 Created by vladutzanu on 2016-09-14 14:52:52 Original: https://sourceforge.net/p/maxima/bugs/3214
Hello
Given the following input:
I ran into some strange results when trying to approximate jacobi_cd() with theta functions. The errors are hinted as early as
_m=0.9, and get bigger from there on. Using jacobi_sn( u + elliptic_kc(m), m ) the results are correct. It's true it's extremely unlikely (I'd say impossible) to get to such a modulus in my quests, but I thought I'd let you know.