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:

RiemannSiegelZ can be used with Interval and CenteredInterval objects:

Compute the elementwise values of an array:

Or compute the matrix RiemannSiegelZ function using MatrixFunction:

Value at zero:

Find the first positive maximum of RiemannSiegelZ[x]:

Plot the RiemannSiegelZ:

Plot the real part of the RiemannSiegelZ function:

Plot the imaginary part of the RiemannSiegelZ function:

Plot the real part of the RiemannSiegelZ function:

Plot the imaginary part of the RiemannSiegelZ function:

RiemannSiegelZ is defined for all real values:

Complex domain:

RiemannSiegelZ is defined through the identity:

RiemannSiegelZ threads elementwise over lists:

RiemannSiegelZ is an analytic function of x:

RiemannSiegelZ is neither non-increasing nor non-decreeing:

RiemannSiegelZ is not injective:

RiemannSiegelZ is neither non-negative nor non-positive:

RiemannSiegelZ does not have singularity or discontinuity:

RiemannSiegelZ is neither convex nor concave:

TraditionalForm formatting:

First derivative with respect to :

Evaluate derivatives numerically:

First and second derivatives with respect to :

Plot the first and second derivatives with respect to :

Find the Taylor expansion using Series:

Plots of the first three approximations around :

Taylor expansion at a generic point:

Series expansion at a singular point: