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SpheroidalPS

SpheroidalPS
gives the angular spheroidal function of the first kind.
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • The angular spheroidal functions satisfy the differential equation with the spheroidal eigenvalue given by SpheroidalEigenvalue.
  • For certain special arguments, SpheroidalPS automatically evaluates to exact values.
  • SpheroidalPS can be evaluated to arbitrary numerical precision.
Evaluate numerically:
Expansion about the spherical case:
Plot :
Evaluate numerically:
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Click for copyable input
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Expansion about the spherical case:
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Click for copyable input
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Plot :
In[1]:=
Click for copyable input
Out[1]=
Evaluate for complex arguments and parameters:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
For certain parameters SpheroidalPS evaluates exactly:
TraditionalForm formatting:
The different types of SpheroidalPS have different branch cut structures:
Solve the spheroidal differential equation in terms of SpheroidalPS:
Plot prolate and oblate versions of the same angular function:
SpheroidalPS is a band-limited function with bandwidth proportional to :
Spheroidal angular harmonics are eigenfunctions of the Sinc transform on the interval :
Spheroidal functions do not evaluate for half-integer values of or generic values of :
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