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MathieuC

MathieuC
gives the even Mathieu function with characteristic value a and parameter q.
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • The Mathieu functions satisfy the equation .
  • For certain special arguments, MathieuC automatically evaluates to exact values.
  • MathieuC can be evaluated to arbitrary numerical precision.
  • MathieuC automatically threads over lists.
Evaluate numerically:
Evaluate numerically:
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Out[1]=
 
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Click for copyable input
Out[1]=
Evaluate for complex arguments and parameters:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
Simple exact values are generated automatically:
MathieuC threads element-wise over lists:
Solve the Schrödinger equation with periodic potential:
By the Bloch theorem, solutions are bounded provided is within an energy band. The energy gap corresponds to a range of where MathieuCharacteristicExponent has a non-vanishing imaginary part:
Solve the Laplace equation in an ellipse using separation of variables:
This finds a zero:
This plots an eigenfunction. It vanishes at the ellipse boundary:
Machine-precision input is insufficient to give a correct answer:
Phase space plots of the Mathieu function:
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