This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.1)

MathieuCharacteristicB

MathieuCharacteristicB
gives the characteristic value for odd Mathieu functions with characteristic exponent r and parameter q.
  • 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 .
Evaluate numerically:
Evaluate numerically:
In[1]:=
Click for copyable input
Out[1]=
 
In[1]:=
Click for copyable input
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:
New in 3