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:

Values at corners of the fundamental cell:

NevilleThetaS for special values of elliptic parameter:

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

Plot the NevilleThetaS functions for various values of the parameter:

Plot NevilleThetaS as a function of its parameter :

Plot the real part of :

Plot the imaginary part of :

The real domain of NevilleThetaS:

The complex domain of NevilleThetaS:

Function range of :

Function range of :

NevilleThetaS 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 for noninteger :

has no singularities or discontinuities for noninteger :

is affine 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 :