Evaluates characteristic values and expansion coefficients.
[ab,c] = mathieu_mathieuf(q,dimM)
the characteristic values with ordering
and
,
for q complex, the ordering is not well-defined.
coefficients of expansions of Periodic Mathieu Functions ce,se,Ce,Se,Fey,Gey,Fek,Gek. c is a matrix: all values of n from -dimM to dimM are calculated.
the parameter(real) of the confocal ellipse family (q=0: circle)
matrix dimension in the calculation (default dimM=10)
Mathieu_mathieuf evaluates characteristic values and expansion coefficients of periodic solutions of the differential equation
(Mathieu equation)
or to solutions of
(Modified Mathieu equation)
// Eigenvalues (imaginary vs. real part) for complex values of q // (see fig. 7 of [1]) for t=0.1:0.2:15 plot( real(2+mathieu_mathieuf(2+t*%i, 6)), imag(mathieu_mathieuf(2+t*%i, 6)), '.'); end xgrid; xtitle('Eigenvalues (imaginary vs. real part) for complex values of q', '$Re[\lambda]$', '$Im[\lambda]$'); | ![]() | ![]() |
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).