Riemann Ξ function

The Riemann Xi function


(where Γ(s) is Euler’s Gamma functionDlmfDlmfMathworldPlanetmath and ζ(s) is the Riemann zeta functionDlmfDlmfMathworldPlanetmath), is the key to the functional equation for the Riemann zeta function.

Riemann himself used the notation of a lower case xi (ξ). The famous Riemann hypothesis is equivalent to the assertion that all the zeros of ξ are real, in fact Riemann himself presented his original hypothesis in terms of that functionMathworldPlanetmath.

Riemann’s lower case xi is defined as

Title Riemann Ξ function
Canonical name RiemannXiFunction
Date of creation 2013-03-22 13:24:06
Last modified on 2013-03-22 13:24:06
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 11
Author PrimeFan (13766)
Entry type Definition
Classification msc 11M06