Evaluate numerically:

Evaluate to high precision:

The precision of the output tracks the precision of the input:

Complex number inputs:

Evaluate efficiently at high precision:

Compute the elementwise values of an array using automatic threading:

Or compute the matrix SpheroidalPS function using MatrixFunction:

Compute average-case statistical intervals using Around:

Evaluate symbolically:

Find the first positive minimum of SpheroidalPS[4,0,1/2,x]:

Evaluate the SpheroidalPS function for half-integer parameters:

Different SpheroidalPS types give different symbolic forms:

Plot the SpheroidalPS function for various orders:

Plot the real part of :

Plot the imaginary part of :

Types 2 and 3 of SpheroidalPS functions have different branch cut structures:

The real domain of :

The complex domain of :

is an even function with respect to :

has the mirror property :

has no singularities or discontinuities:

is neither non-decreasing nor non-increasing:

is not injective:

is neither non-negative nor non-positive:

TraditionalForm formatting:

The first derivative with respect to z:

Higher derivatives with respect to z:

Plot the higher derivatives with respect to z when n=10, m=2 and γ=1/3:

Find the Taylor expansion using Series:

Plots of the first three approximations around :

The Taylor expansion at a generic point: