Mathieu functions toolbox for Scilab

Demos-5

Table of Content

Tables of odd angular Mathieu function and its first derivative

Tables of odd angular Mathieu function and its first derivative

Here we present tables with characteristic values and values of se and se' (z,q) for comparison with [1, Table 20.1, p. 749].

For even orders:

r q b_r se'_r(0, q) se'_r(π/2, q)
2 0 4.00000000 2.0000000e+00 -2.0000000e+00
5 2.09946045 7.3316620e-01 -3.6405179e+00
10 -2.38215824 2.4882284e-01 -4.8634221e+00
15 -8.09934680 9.1819714e-02 -5.7655738e+00
20 -14.49106326 3.7027778e-02 -6.4907522e+00
25 -21.31486062 1.6056217e-02 -7.1067719e+00
10 0 100.00000000 1.0000000e+01 -1.0000000e+01
5 100.12636922 9.7341732e+00 -1.0239646e+01
10 100.50676946 9.4404054e+00 -1.0453948e+01
15 101.14517229 9.1157513e+00 -1.0642900e+01
20 102.04839286 8.7555451e+00 -1.0805724e+01
25 103.22568004 8.3526784e+00 -1.0941354e+01

For odd orders:

r q b_r se'_r(0, q) se_r(π/2, q)
1 0 1.00000000 1.0000000e+00 1.0000000e+00
5 -5.79008060 1.7467540e-01 1.3374339e+00
10 -13.93655248 4.4022566e-02 1.4687557e+00
15 -22.51300350 1.3925135e-02 1.5501151e+00
20 -31.31338617 5.0778849e-03 1.6098916e+00
25 -40.25677898 2.0443594e-03 1.6575104e+00
5 0 25.00000000 5.0000000e+00 1.0000000e+00
5 25.51081605 4.3395700e+00 9.0607793e-01
10 26.76642636 3.4072268e+00 8.4603843e-01
15 27.96788060 2.4116665e+00 8.3794934e-01
20 28.46822133 1.5688969e+00 8.6354312e-01
25 28.06276590 9.6407162e-01 8.9926832e-01
15 0 225.00000000 1.5000000e+01 -1.0000000e+00
5 225.05581248 1.4828789e+01 -9.8896070e-01
10 225.22335697 1.4649860e+01 -9.7814235e-01
15 225.50295624 1.4463001e+01 -9.6751370e-01
20 225.89515342 1.4267946e+01 -9.5704525e-01
25 226.40072004 1.4064373e+01 -9.4670870e-01

This demo uses mathieu_mathieu function.

You can launch it from Scilab menu "? -> Scilab Demonstrations -> Mathieu functions -> Tables of se and se` (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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