SpheroidalQSPrime [n,m,γ,z]
gives the derivative with respect to of the angular spheroidal function of the second kind.
SpheroidalQSPrime
SpheroidalQSPrime [n,m,γ,z]
gives the derivative with respect to of the angular spheroidal function of the second kind.
Details
- Mathematical function, suitable for both symbolic and numerical manipulation.
- SpheroidalQSPrime [n,m,a,γ,z] uses spheroidal functions of type . The types are specified as for SpheroidalPS .
- For certain special arguments, SpheroidalQSPrime automatically evaluates to exact values.
- SpheroidalQSPrime can be evaluated to arbitrary numerical precision.
- SpheroidalQSPrime automatically threads over lists. »
Examples
open all close allBasic Examples (4)
Evaluate numerically:
Expansion about the spherical case:
Plot over a subset of the reals:
Series expansion at the origin:
Scope (22)
Numerical Evaluation (6)
Evaluate numerically:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
Complex number inputs:
Evaluate efficiently at high precision:
Compute the elementwise values of an array using automatic threading:
Or compute the matrix SpheroidalQSPrime function using MatrixFunction :
Compute average-case statistical intervals using Around :
Specific Values (5)
Evaluate symbolically:
Find the first positive minimum of SpheroidalQSPrime [4,0,1/2,x]:
The SpheroidalQSPrime function is equal to zero for half-integer parameters:
Different SpheroidalQSPrime types give different symbolic forms:
TraditionalForm formatting:
Visualization (2)
Plot the SpheroidalQSPrime function for various orders:
Plot the real part of TemplateBox[{1, 0, 1, z}, SpheroidalQSPrime]:
Plot the imaginary part of TemplateBox[{1, 0, 1, z}, SpheroidalQSPrime]:
Function Properties (2)
TemplateBox[{2, 0, 1, x}, SpheroidalQSPrime] has both singularities and discontinuities for :
SpheroidalQSPrime is neither non-negative nor non-positive:
Differentiation (2)
First derivative with respect to z:
Higher derivatives with respect to z:
Plot the higher derivatives with respect to z when n=5, m=2 and γ=1:
Integration (3)
Compute the indefinite integral using Integrate :
Verify the anti-derivative:
Definite integral:
More integrals:
Series Expansions (2)
Find the Taylor expansion using Series :
Plots of the first three approximations around :
Taylor expansion at a generic point:
Applications (1)
Plot prolate and oblate versions of the same angular function:
Possible Issues (1)
Spheroidal functions do not generically evaluate for half-integer values of n:
See Also
Tech Notes
Related Guides
History
Text
Wolfram Research (2007), SpheroidalQSPrime, Wolfram Language function, https://reference.wolfram.com/language/ref/SpheroidalQSPrime.html.
CMS
Wolfram Language. 2007. "SpheroidalQSPrime." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SpheroidalQSPrime.html.
APA
Wolfram Language. (2007). SpheroidalQSPrime. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SpheroidalQSPrime.html
BibTeX
@misc{reference.wolfram_2025_spheroidalqsprime, author="Wolfram Research", title="{SpheroidalQSPrime}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/SpheroidalQSPrime.html}", note=[Accessed: 04-January-2026]}
BibLaTeX
@online{reference.wolfram_2025_spheroidalqsprime, organization={Wolfram Research}, title={SpheroidalQSPrime}, year={2007}, url={https://reference.wolfram.com/language/ref/SpheroidalQSPrime.html}, note=[Accessed: 04-January-2026]}