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BUILT-IN MATHEMATICA SYMBOL

MathieuCharacteristicB

gives the characteristic value

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

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.

Evaluate numerically:

Out[1]=

Out[1]=

Evaluate for complex arguments:

Evaluate to high precision:

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

Simple exact values are generated automatically:

MathieuCharacteristicB threads element-wise over lists:

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):

There is no zero-order MathieuCharacteristicB:

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