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:

Or compute the matrix QBinomial function using MatrixFunction:

QBinomial for symbolic parameters:

Value at zero:

Find the minimum of QBinomial[3,2,q]:

QBinomial threads elementwise over lists:

TraditionalForm formatting:

Plot the QBinomial function for various parameters:

Plot the real part of :

Plot the imaginary part of :

has both singularities and discontinuities for and for :

is neither non-negative nor non-positive:

QBinomial is neither convex nor concave:

TraditionalForm formatting:

The first derivative with respect to n when m=1/2:

The first derivative with respect to m when n=1 and q=2:

Higher derivatives with respect to m:

Plot the higher derivatives with respect to m when n=3 and q=2:

Find the Taylor expansion using Series:

Plots of the first three approximations around :

The Taylor expansion at a generic point: