Bug introduced in 9.0 or earlier and fixed in 10.3.0
This is a documentation mistake in MathieuCharacteristicA
, MathieuCharacteristicB
, and MathieuCharacteristicExponent
.
According to the documentation, the Mathieu characteristic function generates parameter a:
The characteristic value Subscript[a, r] gives the value of the parameter a in y′′+(a-2q cos(2z))y=0 for which the solution has the form e^(i r z) f(z), where f(z) is an even function of z with period 2π.
However, I get the function f
that are periodic of π instead of 2π. Here is the construction of the periodic function f (followed from Input 76 on page 1105 of The Mathematica Guidebook for Symbolics):
f[k_, q_, z_] := (MathieuC[MathieuCharacteristicA[k, q], q, z] + I Sign[k] MathieuS[MathieuCharacteristicB[k, q], q, z])/Exp[I k z]
Plot[{Abs@f[3, -1, z], Abs@f[1/3, -1, z]}, {z, -2 π, 2 π}, Axes -> False, Frame -> True, GridLines -> {π/2 Range[-3, 3, 2], {}}]
So why does the periodic function f
have period of π instead of 2π ?
Pi
. I guess the documentation is wrong. -- Now, should we close this as a "simple mistake in the documentation"? ;P (Unless, I'm wrong, of course.) $\endgroup$MathieuCharacteristicA
,MathieuCharacteristicB
andMathieuCharacteristicExponent
. I was too faithful about the documentation, that I wasted a whole weekend doing completely wrong things :( $\endgroup$MathieuCharacteristicA
in Mathematica but I'm wondering why it only accept integer number as argument. $\endgroup$