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MathieuSPrime

MathieuSPrime
gives the derivative with respect to z of the odd Mathieu function with characteristic value a and parameter q.
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • For certain special arguments, MathieuSPrime automatically evaluates to exact values.
Evaluate numerically:
Evaluate numerically:
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Click for copyable input
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Click for copyable input
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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:
MathieuSPrime threads element-wise over lists:
Mathieu functions arise as solutions of the Laplace equation in an ellipse:
This defines the square of the gradient (the local kinetic energy of a vibrating membrane):
This finds a zero:
This plots the absolute value of the gradient of an eigenfunction:
Phase space plots of the Mathieu function:
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