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 average-case statistical intervals using Around:

Compute the elementwise values of an array:

Or compute the matrix NevilleThetaC function using MatrixFunction:

Values at corners of the fundamental cell:

NevilleThetaC for special values of elliptic parameter:

Find the first positive maximum of NevilleThetaC[x,1/4]:

Different NevilleThetaC types give different symbolic forms:

Plot the NevilleThetaC functions for various values of the parameter:

Plot NevilleThetaC as a function of its parameter :

Plot the real part of :

Plot the imaginary part of :

The real domain of NevilleThetaC:

The complex domain of NevilleThetaC:

Approximate function range of :

Approximate function range of :

NevilleThetaC is an even function:

NevilleThetaC threads elementwise over lists:

is an analytic function of for :

is neither non-decreasing nor non-increasing:

is not injective:

is not surjective:

is neither non-negative nor non-positive, except for :

has no singularities or discontinuities except for :

is affine only for and otherwise it is neither convex nor concave:

Format NevilleThetaC in TraditionalForm:

The first-order derivatives:

Higher-order derivatives:

Plot the higher-order derivatives:

Find the Taylor expansion using Series:

Plots of the first three approximations around :

The Taylor expansion for small elliptic parameter m:

The Taylor expansion around :