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:

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 RiemannSiegelTheta function using MatrixFunction:

Values at zero:

Find the positive minimum of RiemannSiegelTheta[x]:

Plot the RiemannSiegelTheta:

Plot the real part of the RiemannSiegelTheta function:

Plot the imaginary part of the RiemannSiegelTheta function:

RiemannSiegelTheta is defined for all real values:

Complex domain:

Function range of RiemannSiegelTheta:

RiemannSiegelTheta threads elementwise over lists:

RiemannSiegelTheta is an analytic function of x:

RiemannSiegelTheta is non-increasing in a specific range:

RiemannSiegelTheta is not injective:

RiemannSiegelTheta is surjective:

RiemannSiegelTheta is neither non-negative nor non-positive:

RiemannSiegelTheta has no singularities or discontinuities:

RiemannSiegelTheta is neither convex nor concave:

TraditionalForm formatting:

First derivative with respect to :

Higher derivatives with respect to :

Plot the higher derivatives with respect to :

Formula for the derivative with respect to :

Find the Taylor expansion using Series:

Plots of the first three approximations around :

Find the series expansion at Infinity:

Find the series expansion for an arbitrary symbolic direction :

Taylor expansion at a generic point: