Riemann xi-function

The xi-function is the function ξ(z) | congruent | 1/2 z(z - 1)(Γ(1/2 z))/π^(z/2) ζ(z) | = | ((z - 1) Γ(1/2 z + 1) ζ(z))/sqrt(π^z), where ζ(z) is the Riemann zeta function and Γ(z) is the gamma function. This is a variant of the function originally defined by Riemann in his landmark paper, where the above now standard notation follows Landau. It is an entire function. It is implemented in the Wolfram Language as RiemannXi[s].

de Bruijn-Newman constant | Lehmer's phenomenon | Li's criterion | Riemann hypothesis | Riemann-Siegel functions | Riemann-Siegel integral formula | Riemann zeta function | Riemann zeta function zeros