- Mathematical function, suitable for symbolic and numeric manipulations.
- For certain special arguments, RiemannXi automatically evaluates to exact values.
- RiemannXi is an entire function with no branch cut discontinuities.
- RiemannXi can be evaluated to arbitrary numerical precision.
- RiemannXi automatically threads over lists.
Examplesopen allclose all
Basic Examples (6)
Plot over a subset of the reals:
Plot over a subset of the complexes:
Series expansion at the origin:
Series expansion at Infinity:
Series expansion at a singular point:
Numerical Evaluation (4)
Evaluate to high precision:
The precision of the output tracks the precision of the input:
Complex number inputs:
Evaluate efficiently at high precision:
Specific Values (4)
Simple exact values are generated automatically:
Value at zero:
Find the minimum of RiemannXi[x]:
First derivative with respect to :
Higher derivatives with respect to :
Plot the higher derivatives with respect to :
Formula for the derivative with respect to :
Series Expansions (4)
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:
Introduced in 2014