Mathieu functions toolbox for Scilab

Demos-4

Table of Content

Tables of even angular Mathieu function and its first derivative

Tables of even angular Mathieu function and its first derivative

Here we present tables with characteristic values and values of ce and ce' (z,q) for comparison with [1, Table 20.1, p. 748].

For even orders:

r q a_r ce_r(0, q) ce_r(π/2, q)
0 0 0.00000000 7.07106781e-01 7.0710678e-01
5 -5.80004602 4.48001817e-02 1.3348487e+00
10 -13.93697996 7.62651757e-03 1.4686605e+00
15 -22.51303776 1.93250832e-03 1.5501081e+00
20 -31.31339007 6.03743829e-04 1.6098909e+00
25 -40.25677955 2.15863018e-04 1.6575103e+00
2 0 4.00000000 1.00000000e+00 -1.0000000e+00
5 7.44910974 7.35294308e-01 -7.2448815e-01
10 7.71736985 2.45888349e-01 -9.2675926e-01
15 5.07798320 7.87928278e-02 -1.0199662e+00
20 1.15428289 2.86489431e-02 -1.0752932e+00
25 -3.52216473 1.15128663e-02 -1.1162790e+00
10 0 100.00000000 1.00000000e+00 -1.0000000e+00
5 100.12636922 1.02599503e+00 -9.7534749e-01
10 100.50677002 1.05381599e+00 -9.5164532e-01
15 101.14520345 1.08410631e+00 -9.2854806e-01
20 102.04891602 1.11778863e+00 -9.0571078e-01
25 103.23020480 1.15623992e+00 -8.8269191e-01

For odd orders:

r q a_r ce_r(0, q) ce'_r(π/2, q)
1 0 1.00000000 1.00000000e+00 -1.0000000e+00
5 1.85818754 2.56542879e-01 -3.4690420e+00
10 -2.39914240 5.35987477e-02 -4.8504383e+00
15 -8.10110513 1.50400665e-02 -5.7642064e+00
20 -14.49130143 5.05181376e-03 -6.4905658e+00
25 -21.31489969 1.91105151e-03 -7.1067412e+00
5 0 25.00000000 1.00000000e+00 -5.0000000e+00
5 25.54997175 1.12480725e+00 -5.3924862e+00
10 27.70376873 1.25801994e+00 -5.3212765e+00
15 31.95782125 1.19343223e+00 -5.1191499e+00
20 36.64498973 9.36575531e-01 -5.7786753e+00
25 40.05019099 6.10694310e-01 -7.0598843e+00
15 0 225.00000000 1.00000000e+00 1.5000000e+01
5 225.05581248 1.01129373e+00 1.5163657e+01
10 225.22335697 1.02287828e+00 1.5319880e+01
15 225.50295624 1.03479365e+00 1.5468744e+01
20 225.89515342 1.04708434e+00 1.5610279e+01
25 226.40072004 1.05980044e+00 1.5744473e+01

This demo uses mathieu_mathieu function.

You can launch it from Scilab menu "? -> Scilab Demonstrations -> Mathieu functions -> Tables of ce and ce` (z,q) for comparison with Abramowitz and Stegun".

Bibliography

  1. M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions, Dover, New York, 1965.

Created: 5 years 3 months ago
by Nikolay Strelkov

Updated: 5 years 3 months ago
by Nikolay Strelkov

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