MathieuCharacteristicA
gives the characteristic value for even 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 even function of
with period
.
- For certain special arguments, MathieuCharacteristicA automatically evaluates to exact values.
- MathieuCharacteristicA can be evaluated to arbitrary numerical precision.
- MathieuCharacteristicA automatically threads over lists.
Examples
open allclose allBasic Examples (3)
Scope (16)
Numerical Evaluation (4)
Specific Values (2)
Simple exact values are generated automatically:
Find the positive maximum of MathieuCharacteristicA[2,q ]:
Visualization (3)
Plot the MathieuCharacteristicA function for integer parameters:
Plot the MathieuCharacteristicA function for noninteger parameters:
Plot the real part of MathieuCharacteristicA:
Plot the imaginary part of MathieuCharacteristicA:
Function Properties (7)
The real domain of MathieuCharacteristicA:
Approximate function range of :
is neither non-increasing nor non-decreasing:
MathieuCharacteristicA 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, MathieuCharacteristicA 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:
Properties & Relations (1)
MathieuCharacteristicA is a special case of SpheroidalEigenvalue:
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