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gives the radial spheroidal function of the first kind.
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • The radial spheroidal functions satisfy the differential equation with the spheroidal eigenvalue given by SpheroidalEigenvalue.
  • The are normalized according to the Meixner-Schäfke scheme.
  • SpheroidalS1 can be evaluated to arbitrary numerical precision.
Evaluate numerically:
Evaluate numerically:
Click for copyable input
Evaluate for complex arguments and parameters:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
For certain parameters SpheroidalS1 evaluates exactly:
TraditionalForm typesetting:
Spheroidal angular harmonics are eigenfunctions of the Sinc transform on the interval :
Plot the eigenvalue:
Find resonant frequencies for the Dirichlet problem in the prolate spheroidal cavity:
Determine the first few frequencies:
Plot the prolate and oblate functions:
Spheroidal functions do not evaluate for half-integer values of and generic values of :
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