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SpheroidalEigenvalue

SpheroidalEigenvalue
gives the spheroidal eigenvalue with degree and order .
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • The spheroidal eigenvalues for successive correspond to the successive values of for which there exist normalizable solutions to the differential equation .
Evaluate numerically:
Series expansion in the spherical limit:
Evaluate numerically:
In[1]:=
Click for copyable input
Out[1]=
 
Series expansion in the spherical limit:
In[1]:=
Click for copyable input
Out[1]=
Evaluate for complex arguments:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
SpheroidalEigenvalue threads element-wise over lists:
For certain parameters SpheroidalEigenvalue evaluates exactly:
TraditionalForm formatting:
Solve the spheroidal differential equation:
Find a branch point of SpheroidalEigenvalue:
SpheroidalEigenvalue does not evaluate for half-integer or for generic :
The half-integer values of are singular for the near-spherical expansion:
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