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 NevilleThetaN function using MatrixFunction:

Values at corners of the fundamental cell:

NevilleThetaN for special values of elliptic parameter:

Find the first positive maximum of NevilleThetaN[x,1/2]:

Plot the NevilleThetaN functions for various values of the parameter:

Plot NevilleThetaN as a function of its parameter :

Plot the real part of :

Plot the imaginary part of :

The real domain of NevilleThetaN:

The complex domain of NevilleThetaN:

Function range of :

Function range of :

NevilleThetaN is an even function:

NevilleThetaN vanishes at :

NevilleThetaN threads elementwise over lists:

is an analytic function of for :

is neither non-decreasing nor non-increasing:

is not injective:

is not surjective:

is non-negative for noninteger m:

has no singularities or discontinuities for noninteger m:

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

TraditionalForm formatting:

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 :

The Taylor expansion around :