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MathieuCharacteristicA strange behaviour

  • To: mathgroup at smc.vnet.net
  • Subject: [mg115087] MathieuCharacteristicA strange behaviour
  • From: "Jose M. Castelo" <jocasa at alumni.uv.es>
  • Date: Thu, 30 Dec 2010 06:29:03 -0500 (EST)

Hi!

I'm working with the Mathematica function 'MathieuCharacteristicA[r,q]' 
which gives the characteristic value for even Mathieu functions with 
characteristic exponent r and parameter q.

After testing with various commands which deal with computation 
precision I have been unable to obtain a good behaviour of the function 
for some values of q and some ranges of r. You can see that the function 
does strange things by ploting it against r:

Plot[MathieuCharacteristicA[r, 100], {r, 10, 17}]
Plot[MathieuCharacteristicA[r, 8652.34], {r, 140, 150}]

The curve jumps abruptly where it should be smooth. I don't mean the 
zones where the function is staircase like, I know that is the right 
shape it should have. The same happens with 'MathieuCharacteristicB[r,q]'.

Perhaps I am missing some precision detail in the plot, or in the 
selfsame function, though I have tried to solve it unsuccessfully by 
using precision related commands. Perhaps it is a bug.

Could you tell me if you get the same results? Maybe you can throw some 
light on how to get it work correctly, as the very same 
'MathieuC[a,q,z]' and 'MathieuS[a,q,z]' functions depend on the 
characteristic value 'a' directly, not on the characteristic exponent 
'r' as I think should be better. In that way they inherit the error of 
the characteristic value computation.

If this is not the right place to post a message about Mathematica bugs, 
please let me know where to post it.

Thanks a lot,

Jose


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