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SpheroidalQS

SpheroidalQS
gives the angular spheroidal function of the second 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, SpheroidalQS automatically evaluates to exact values.
  • SpheroidalQS 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 :
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Click for copyable input
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Evaluate for complex arguments and parameters:
Evaluate to high precision:
The precision of the output tracks the precision of the input:
For certain parameters SpheroidalQS evaluates exactly:
TraditionalForm formatting:
The different types of SpheroidalQS have different branch cut structures:
Solve the spheroidal differential equation in terms of SpheroidalQS:
Plot prolate and oblate versions of the same angular function:
Spheroidal functions do not generically evaluate for half-integer values of :
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