@ecterrab 

Hi,

I actually have the same question as @strokebow 10 does.

In physics, Mathieu functions are strongly related to the Schrodinger equation for a periodic potential. If my understanding is correct, the Mathieu characteristic function seems to correspond to the band structrue of this periodic potential, and should be defined at non-integer as well.

For example, Mathematica can calculate the Mathieu characteristic function for non integers and make a plot

Plot[MathieuCharacteristicA[r, 1], {r, -2.5, 2.5}]

Could you explain what are the differences of the Mathieu functions between Mathematica and Maple, and could Maple produce a similer plot for the Mathieu characteristic function?

Thanks.