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 SpheroidalQS function using MatrixFunction:

Compute average-case statistical intervals using Around:

SpheroidalQS[n,m,0,x] is equivalent to the LegendreQ[n,m,x] function:

Find the first positive maximum of SpheroidalQS[4,0,1/2,x]:

The SpheroidalQS function is equal to zero for half-integer parameters:

Different SpheroidalQS types give different symbolic forms:

Plot the SpheroidalQS function for various orders:

Plot the real part of :

Plot the imaginary part of :

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

is an even function:

has both singularities and discontinuities for :

is neither non-decreasing nor non-increasing:

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=5, m=2 and γ=1:

Find the Taylor expansion using Series:

Plots of the first three approximations around :

The Taylor expansion at a generic point: