MathieuCharacteristicB

MathieuCharacteristicB[r,q]

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

Details

Examples

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Basic Examples  (3)

Evaluate numerically:

Plot over a subset of the reals:

Plot over a subset of the complexes:

Scope  (11)

Numerical Evaluation  (4)

Evaluate numerically:

Evaluate to high precision:

The precision of the output tracks the precision of the input:

Complex number inputs:

Evaluate efficiently at high precision:

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)

The real domain of MathieuCharacteristicB:

MathieuCharacteristicB threads elementwise over lists:

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:

Neat Examples  (1)

Branch points of the Mathieu characteristic along the imaginary q axis:

Introduced in 1996
 (3.0)