gives the derivative with respect to of the radial spheroidal function of the second kind.
- Mathematical function, suitable for both symbolic and numerical manipulation.
- For certain special arguments, SpheroidalS2Prime automatically evaluates to exact values.
- SpheroidalS2Prime can be evaluated to arbitrary numerical precision.
- SpheroidalS2Prime automatically threads over lists.
Examplesopen allclose all
Basic Examples (5)
Plot over a subset of the reals:
Plot over a subset of the complexes:
Series expansion at the origin:
Series expansion at a singular point:
Numerical Evaluation (4)
Evaluate to high precision:
The precision of the output tracks the precision of the input:
Complex number inputs:
Evaluate efficiently at high precision:
First derivative with respect to :
Higher derivatives with respect to :
Plot the higher derivatives with respect to when , and :
Compute the indefinite integral using Integrate:
Verify the anti-derivative:
Series Expansions (2)
Find the Taylor expansion using Series:
Plots of the first three approximations around :
Taylor expansion at a generic point:
Properties & Relations (1)
Spheroidal functions do not evaluate for half-integer values of and generic values of :