Evaluate to high precision:

The precision of the output tracks the precision of the input:

Evaluate for complex arguments and parameters:

Evaluate JacobiZeta efficiently at high precision:

Compute worst-case guaranteed intervals using Interval and CenteredInterval objects:

Or compute average-case statistical intervals using Around:

Compute the elementwise values of an array:

Or compute the matrix JacobiZeta function using MatrixFunction:

Simple exact results are generated automatically:

Exact values after FunctionExpand is applied:

Value at infinity:

Find a local maximum as a root of :

JacobiZeta is an odd function with respect to the first argument:

Plot JacobiZeta as a function of its first parameter :

Plot JacobiZeta as a function of its second parameter :

Plot the real part of :

Plot the imaginary part of :

JacobiZeta is not an analytic function:

However, for fixed , is an analytic function of :

Thus, for example, has no singularities or discontinuities:

is neither nondecreasing nor nonincreasing:

is not injective:

is not surjective:

is neither non-negative nor non-positive:

is neither convex nor concave:

First derivative:

Higher derivatives:

Plot higher derivatives for :

Differentiate with respect to its second parameter :

Definite integral of an odd function over an interval centered at the origin:

Taylor expansion for JacobiZeta:

Plot the first three approximations for around :

Taylor expansion at the origin in the parameter :

Plot the first three approximations for around :

Find series expansions at a branch point:

JacobiZeta can be applied to a power series:

Primary definition:

Relation to other elliptic‐type functions:

TraditionalForm formatting: