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mathieu_mathieu

Evaluates periodic Mathieu functions.

Calling Sequence

[y, ab] = mathieu_mathieu(kind, n, z, q [, prec])

Parameters

kind

'ce', 'se', 'ce_' (ce first derivative), 'se_' (se first derivative), 'Ce', 'Se', ('Fy', 'Gy', 'Fk', 'Gk' not yet)

n

the order, an array of positive integers

z

the argument, a real row vector

q

parameter of the confocal ellipse family (q=0 : circle)

prec

(optional) the precision (default 1e-3)

y

value of corresponding Mathieu function

ab

the characteristic values with ordering and , for q complex, the ordering is not well-defined.

Description

Mathieu_mathieu evaluates periodic Mathieu functions by calling mathieu_mathieuf

Examples

// 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;

See Also

Used Functions

besselj

Authors

R.Coisson and G. Vernizzi, Parma University

X. K. Yang

N. O. Strelkov, NRU MPEI

2011 - DIGITEO - Michael Baudin

Bibliography

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).


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