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MathieuCPrime[a,q,z]

gives the derivative with respect to z of the even Mathieu function with characteristic value a and parameter q.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Numerical Evaluation  
Specific Values  
Visualization  
Function Properties  
Differentiation  
Series Expansions  
Applications  
Neat Examples  
See Also
Tech Notes
Related Guides
Related Links
History
Cite this Page

MathieuCPrime

MathieuCPrime[a,q,z]

gives the derivative with respect to z of the even Mathieu function with characteristic value a and parameter q.

Details

  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • For certain special arguments, MathieuCPrime automatically evaluates to exact values.
  • MathieuCPrime can be evaluated to arbitrary numerical precision.
  • MathieuCPrime automatically threads over lists.

Examples

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Basic Examples  (4)

Evaluate numerically:

Plot over a subset of the reals:

Plot over a subset of the complexes:

Series expansion about the origin:

Scope  (19)

Numerical Evaluation  (5)

Evaluate numerically to high precision:

The precision of the output tracks the precision of the input:

Evaluate for complex arguments and parameters:

Evaluate MathieuCPrime efficiently at high precision:

MathieuCPrime threads elementwise over lists:

Compute the elementwise values of an array:

Or compute the matrix MathieuCPrime function using MatrixFunction:

Specific Values  (3)

Simple exact values are generated automatically:

Find a zero of MathieuCPrime:

MathieuCPrime is an odd function:

Visualization  (2)

Plot the MathieuCPrime function:

Plot the real part of MathieuCPrime for and :

Plot the imaginary part of MathieuCPrime for and :

Function Properties  (4)

MathieuCPrime has singularities and discontinuities when the characteristic exponent is an integer:

is neither nondecreasing nor nonincreasing:

MathieuCPrime is neither non-negative nor non-positive:

MathieuCPrime is neither convex nor concave:

Differentiation  (3)

First derivative:

Higher derivatives:

Plot higher derivatives for and :

Plot higher derivatives for and :

MathieuCPrime is the derivative of MathieuC:

Series Expansions  (2)

Taylor expansion:

Plot the first three approximations for MathieuCPrime around :

Taylor expansion of MathieuCPrime at a generic point:

Applications  (1)

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:

Neat Examples  (1)

Phase space plots of the Mathieu function:

Wolfram Research (1996), MathieuCPrime, Wolfram Language function, https://reference.wolfram.com/language/ref/MathieuCPrime.html.

Text

Wolfram Research (1996), MathieuCPrime, Wolfram Language function, https://reference.wolfram.com/language/ref/MathieuCPrime.html.

CMS

Wolfram Language. 1996. "MathieuCPrime." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/MathieuCPrime.html.

APA

Wolfram Language. (1996). MathieuCPrime. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MathieuCPrime.html

BibTeX

@misc{reference.wolfram_2025_mathieucprime, author="Wolfram Research", title="{MathieuCPrime}", year="1996", howpublished="\url{https://reference.wolfram.com/language/ref/MathieuCPrime.html}", note=[Accessed: 08-August-2025]}

BibLaTeX

@online{reference.wolfram_2025_mathieucprime, organization={Wolfram Research}, title={MathieuCPrime}, year={1996}, url={https://reference.wolfram.com/language/ref/MathieuCPrime.html}, note=[Accessed: 08-August-2025]}