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BUILT-IN MATHEMATICA SYMBOL

SpheroidalQS

gives the angular spheroidal function

of the second kind.

The angular spheroidal functions satisfy the differential equation with the spheroidal eigenvalue given by SpheroidalEigenvalue.

SpheroidalQS gives spheroidal functions of type . The types are specified as for LegendreP.

For certain special arguments, SpheroidalQS automatically evaluates to exact values.

Evaluate numerically:

Expansion about the spherical case:

Plot

Evaluate numerically:

Out[1]=

Expansion about the spherical case:

Out[1]=

Plot

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 SpheroidalQS evaluates exactly:

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