MathieuSPrime
MathieuSPrime[a,q,z]
gives the derivative with respect to z of the odd Mathieu function with characteristic value a and parameter q.
Details

- Mathematical function, suitable for both symbolic and numerical manipulation.
- For certain special arguments, MathieuSPrime automatically evaluates to exact values.
- MathieuSPrime can be evaluated to arbitrary numerical precision.
- MathieuSPrime automatically threads over lists.
Examples
open allclose allBasic Examples (4)
Scope (18)
Numerical Evaluation (4)
Evaluate numerically to high precision:
The precision of the output tracks the precision of the input:
Evaluate for complex arguments and parameters:
Evaluate MathieuSPrime efficiently at high precision:
MathieuSPrime threads elementwise over lists:
Specific Values (3)
Simple exact values are generated automatically:
Find a zero of MathieuSPrime:
MathieuSPrime is an even function:
Visualization (2)
Plot the MathieuSPrime function:
Plot the real part of MathieuSPrime for and
:
Plot the imaginary part of MathieuSPrime for and
:
Function Properties (4)
MathieuSPrime has singularities and discontinuities when the characteristic exponent is an integer:
is neither nondecreasing nor nonincreasing:
MathieuSPrime is neither non-negative nor non-positive:
MathieuSPrime is neither convex nor concave:
Differentiation (3)
Plot higher derivatives for and
:
Plot higher derivatives for and
:
MathieuSPrime is the derivative of MathieuS:
Series Expansions (2)
Plot the first three approximations for MathieuSPrime around :
Taylor expansion of MathieuSPrime at a generic point:
Applications (1)
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