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:

Value at zero:

WeierstrassSigma automatically evaluates to simpler functions for certain parameters:

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

Plot the WeierstrassSigma function for various parameters:

Plot the real part of :

Plot the imaginary part of :

WeierstrassSigma is defined for all real and complex inputs:

Approximate function range of :

WeierstrassSigma is an odd function with respect to x:

WeierstrassSigma threads elementwise over lists in its first argument:

is an analytic function of :

It has no singularities or 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 :

Find the Taylor expansion using Series:

Plots of the first three approximations around :

Find series expansion for an arbitrary symbolic direction :

Taylor expansion at a generic point: