Mathieu Function Plots

We plot Mathieu functions for q = 1 and 10 in order to show the periodic and anti-periodic properties of the sine-elliptic and cosine-elliptic solutions.

The plots were inspired by the NIST Digital Library of Mathematical Functions.

The code used to generate these plots is also available in the example folder of the package.

# Plot of various Mathieu functions, inspired by https://dlmf.nist.gov/28.3
using Mathieu, PyPlot
const MPL = PyPlot.matplotlib

# get the same line colors
PyPlot.PyDict(MPL."rcParams")["axes.prop_cycle"] =
    MPL.cycler(color=["#2ca02c","#d62728","#1f77b4","#ff7f0e"])

# plot parameters
z = LinRange(0,π/2,101)
n = 0:3

for q in [1,10]
    f,ax = subplots(2,2,figsize=(10,8));
    f.suptitle("Mathieu Functions for \$q=$q\$");

    ax[1].set_title("Even π-Periodic Solutions");
    ax[1].plot(z, Mathieu.cep(n,q,z));
    ax[1].legend(string.("\$ce_",2n,"\$"));

    ax[2].set_title("Even π-Antiperiodic Solutions");
    ax[2].plot(z, Mathieu.cea(n,q,z));
    ax[2].legend(string.("\$ce_",2n.+1,"\$"));

    ax[3].set_title("Odd π-Antiperiodic Solutions");
    ax[3].plot(z, Mathieu.sea(n,q,z));
    ax[3].legend(string.("\$se_",2n.+1,"\$"));

    ax[4].set_title("Odd π-Periodic Solutions");
    ax[4].plot(z, Mathieu.sep(n,q,z));
    ax[4].legend(string.("\$se_",2n.+2,"\$"));
end