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