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:

RiemannXi can be used with Interval and CenteredInterval objects:

Simple exact values are generated automatically:

Value at zero:

Evaluate symbolically:

Find the minimum of RiemannXi[x]:

Plot the RiemannXi:

Plot the real part of the RiemannXi function:

Plot the imaginary part of the RiemannXi function:

RiemannXi has the mirror property :

RiemannXi is defined through the identity:

RiemannXi threads element‐wise over lists:

RiemannXi is neither non-increasing nor non-decreeing:

RiemannXi is not an injective function:

TraditionalForm formatting, while avoiding the evaluation:

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: