MathieuCharacteristicB
gives the characteristic value for odd Mathieu functions with characteristic exponent r and parameter q.
Details

- Mathematical function, suitable for both symbolic and numerical manipulation.
- The characteristic value
gives the value of the parameter
in
for which the solution has the form
where
is an odd function of
with period
.
- When r is not a real integer, MathieuCharacteristicB gives the same results as MathieuCharacteristicA.
- For certain special arguments, MathieuCharacteristicB automatically evaluates to exact values.
- MathieuCharacteristicB can be evaluated to arbitrary numerical precision.
- MathieuCharacteristicB automatically threads over lists.
Examples
open allclose allBasic Examples (3)
Scope (15)
Numerical Evaluation (4)
Specific Values (2)
Simple exact values are generated automatically:
Find the positive maximum of MathieuCharacteristicB[3,q]:
Visualization (3)
Plot the MathieuCharacteristicB function for integer parameters:
Plot the MathieuCharacteristicB function for noninteger parameters:
Plot the real part of MathieuCharacteristicB:
Plot the imaginary part of MathieuCharacteristicB:
Function Properties (6)
The real domain of MathieuCharacteristicB:
is neither non-increasing nor non-decreasing:
MathieuCharacteristicB threads elementwise over lists:
TraditionalForm formatting:
Applications (4)
Symmetric periodic solutions of the Mathieu differential equation:
This shows the stability diagram for the Mathieu equation:
As a function of the first argument, MathieuCharacteristicB is a piecewise continuous function (called bands and band gaps in solid-state physics):
Solve the Laplace equation in an ellipse using separation of variables:
This plots an eigenfunction. It vanishes at the ellipse boundary:
Possible Issues (1)
There is no zero-order MathieuCharacteristicB:

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