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MathieuCharacteristicA

MathieuCharacteristicA
gives the characteristic value for even 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 even function of with period .
Evaluate numerically:
Evaluate numerically:
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Click for copyable input
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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:
MathieuCharacteristicA 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, MathieuCharacteristicA is a piecewise continuous function (called bands and band gaps in solid state physics):
Branch points of the Mathieu characteristic along the imaginary q axis:
New in 3