SpheroidalPS

SpheroidalPS[n,m,γ,z]

gives the angular spheroidal function of the first kind.

Details

  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • The angular spheroidal functions satisfy the differential equation with the spheroidal eigenvalue given by SpheroidalEigenvalue[n,m,γ].
  • SpheroidalPS[n,m,0,z] is equivalent to LegendreP[n,m,z].
  • SpheroidalPS[n,m,a,γ,z] gives spheroidal functions of type . The types are specified as for LegendreP.
  • For certain special arguments, SpheroidalPS automatically evaluates to exact values.
  • SpheroidalPS can be evaluated to arbitrary numerical precision.
  • SpheroidalPS automatically threads over lists.

Examples

open allclose all

Basic Examples  (3)

Evaluate numerically:

In[1]:=
Click for copyable input
Out[1]=

Expansion about the spherical case:

In[1]:=
Click for copyable input
Out[1]=

Plot :

In[1]:=
Click for copyable input
Out[1]=

Scope  (5)

Generalizations & Extensions  (1)

Applications  (3)

Properties & Relations  (1)

Possible Issues  (1)

See Also

LegendreP  SpheroidalQS

Tutorials

Introduced in 2007
(6.0)