Evaluates periodic Mathieu functions.
[y, ab] = mathieu_mathieu(kind, n, z, q [, prec])
'ce', 'se', 'ce_' (ce first derivative), 'se_' (se first derivative), 'Ce', 'Se', ('Fy', 'Gy', 'Fk', 'Gk' not yet)
the order, an array of positive integers
the argument, a real row vector
parameter of the confocal ellipse family (q=0 : circle)
(optional) the precision (default 1e-3)
value of corresponding Mathieu function
the characteristic values with ordering
and
,
for q complex, the ordering is not well-defined.
Mathieu_mathieu evaluates periodic Mathieu functions by calling mathieu_mathieuf
// se1 functions with different values of q // (see fig. 4 of [1]) z = linspace(0, 2*%pi, 100); plot(z, mathieu_mathieu('se', 1, z, 0.1)', 'b', z, mathieu_mathieu('se', 1, z, 1)', 'g', ... z, mathieu_mathieu('se', 1, z, 5)', 'r', z, mathieu_mathieu('se', 1, z, 20)', 'c'); legend('$q = 0.1$','$q = 1$','$q = 5$','$q = 20$'); xgrid; xtitle('$se_1\ \text{functions\ with\ different}\ q$','$z$','$se_1$'); h = gca(); font_sz = 4; h.font_size = font_sz; h.title.font_size=font_sz; h.x_label.font_size=font_sz; h.y_label.font_size=font_sz; h.children(1).font_size = font_sz; | ![]() | ![]() |
besselj
R.Coisson and G. Vernizzi, Parma University
X. K. Yang
N. O. Strelkov, NRU MPEI
2011 - DIGITEO - Michael Baudin
1. R. Coïsson, G. Vernizzi and X.K. Yang, "Mathieu functions and numerical solutions of the Mathieu equation", IEEE Proceedings of OSSC2009 (online at http://www.fis.unipr.it/~coisson/Mathieu.pdf).