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:

Series expansion about the origin:

Special values:

Related functions:   zeta

Function category: zeta functions sagemath-docs