zeta_symmetric( n , z )

The symmetric Riemann ξ-function of z in SageMath. Defined by

$\xi (z) = \frac{ z(z-1) }{ 2 } \Gamma \left( \frac{ z }{ 2 } \right) \pi^{ -z/2 } \zeta (z)$

Satisfies $$\xi (z) = \xi (1-z)$$.

Plot on the real axis: