SEARCH MATHEMATICA 8 DOCUMENTATION

THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION.

Built-in Mathematica Symbol

MathieuCharacteristicB

MathieuCharacteristicB[r, q]
gives the characteristic value b_r for odd Mathieu functions with characteristic exponent r and parameter q.

The characteristic value b_r gives the value of the parameter a in for which the solution has the form where is an odd function of z 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:

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: