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:

WeierstrassZeta can be used with CenteredInterval objects:

Compute average-case statistical intervals using Around:

Compute the elementwise values of an array:

Or compute the matrix WeierstrassZeta function using MatrixFunction:

Value at zero:

WeierstrassZeta automatically evaluates to simpler functions for certain parameters:

Find a value of x for which WeierstrassZeta[x,1/2,1/2]=3:

Plot the WeierstrassZeta function for various parameters:

Plot the real part of :

Plot the imaginary part of :

Real domain of WeierstrassZeta:

WeierstrassZeta is an odd function with respect to x:

WeierstrassZeta threads elementwise over lists in its first argument:

WeierstrassZeta is not an analytic function:

It has both singularities and discontinuities:

is neither nondecreasing nor nonincreasing:

is not injective:

is surjective:

is neither non-negative nor non-positive:

is neither convex nor concave:

TraditionalForm formatting:

First derivative with respect to :

Higher derivatives with respect to :

Plot the higher derivatives with respect to :

Compute the indefinite integral using Integrate:

Verify the anti-derivative:

Definite integral:

More integrals:

Find the Taylor expansion using Series:

Plots of the first three approximations around :

Find the series expansion for an arbitrary symbolic direction :

Taylor expansion at a generic point: