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 (11)
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 (2)
Applications (3)
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):
Possible Issues (1)
There is no zero-order MathieuCharacteristicB:
