SpheroidalPSPrime[n,m,γ,z]
gives the derivative with respect to of the angular spheroidal function
of the first kind.


SpheroidalPSPrime
SpheroidalPSPrime[n,m,γ,z]
gives the derivative with respect to of the angular spheroidal function
of the first kind.
Details

- Mathematical function, suitable for both symbolic and numerical manipulation.
- SpheroidalPSPrime[n,m,a,γ,z] uses spheroidal functions of type
. The types are specified as for SpheroidalPS.
- For certain special arguments, SpheroidalPSPrime automatically evaluates to exact values.
- SpheroidalPSPrime can be evaluated to arbitrary numerical precision.
- SpheroidalPSPrime automatically threads over lists. »
Examples
open all close allBasic Examples (6)
Expansion about the spherical case:
Plot over a subset of the reals:
Series expansion at the origin:
Series expansion at Infinity:
Scope (28)
Numerical Evaluation (6)
The precision of the output tracks the precision of the input:
Evaluate efficiently at high precision:
Compute the elementwise values of an array using automatic threading:
Or compute the matrix SpheroidalPSPrime function using MatrixFunction:
Compute average-case statistical intervals using Around:
Specific Values (4)
Find the first positive minimum of SpheroidalPSPrime[4,0,1/2,x]:
Evaluate the SpheroidalPSPrime function for half-integer parameters:
Different SpheroidalPSPrime types give different symbolic forms:
Visualization (3)
Plot the SpheroidalPSPrime function for various orders:
Types 2 and 3 of SpheroidalPSPrime functions have different branch cut structures:
Function Properties (8)
is an even function with respect to
:
has no singularities or discontinuities:
is neither non-decreasing nor non-increasing:
is neither non-negative nor non-positive:
TraditionalForm formatting:
Differentiation (2)
Integration (3)
Compute the indefinite integral using Integrate:
Series Expansions (2)
Find the Taylor expansion using Series:
Generalizations & Extensions (1)
SpheroidalPSPrime of different types have different branch cut structures:
See Also
Tech Notes
Related Guides
History
Text
Wolfram Research (2007), SpheroidalPSPrime, Wolfram Language function, https://reference.wolfram.com/language/ref/SpheroidalPSPrime.html.
CMS
Wolfram Language. 2007. "SpheroidalPSPrime." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SpheroidalPSPrime.html.
APA
Wolfram Language. (2007). SpheroidalPSPrime. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SpheroidalPSPrime.html
BibTeX
@misc{reference.wolfram_2025_spheroidalpsprime, author="Wolfram Research", title="{SpheroidalPSPrime}", year="2007", howpublished="\url{https://reference.wolfram.com/language/ref/SpheroidalPSPrime.html}", note=[Accessed: 13-August-2025]}
BibLaTeX
@online{reference.wolfram_2025_spheroidalpsprime, organization={Wolfram Research}, title={SpheroidalPSPrime}, year={2007}, url={https://reference.wolfram.com/language/ref/SpheroidalPSPrime.html}, note=[Accessed: 13-August-2025]}