MathieuCPrime [a,q,z]
gives the derivative with respect to z of the even Mathieu function with characteristic value a and parameter q.
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
open all close allBasic 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:
See Also
Tech Notes
Related Guides
Related Links
History
Introduced in 1996 (3.0)
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: 17-November-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: 17-November-2025]}