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 allclose allBasic Examples (7)
Expansion about the spherical case:
Plot over a subset of the reals:
Plot over a subset of the complexes:
Series expansion at the origin:
Series expansion at Infinity:
Scope (22)
Numerical Evaluation (4)
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 (4)
The real domain of SpheroidalPSPrime:
The complex domain of SpheroidalPSPrime:
SpheroidalPSPrime is even function with respect to γ:
SpheroidalPSPrime has the mirror property :
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:
Text
Wolfram Research (2007), SpheroidalPSPrime, Wolfram Language function, https://reference.wolfram.com/language/ref/SpheroidalPSPrime.html.
BibTeX
BibLaTeX
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