The xi-function is the function
 |  |  |
(1)
|
 |  |  |
(2)
|
where 
is the Riemann zeta function and 
is the gamma function
(Gradshteyn and Ryzhik 2000, p. 1076; Hardy 1999, p. 41; Edwards 2001,
p. 16). This is a variant of the function originally defined by Riemann in his
landmark paper (Riemann 1859), where the above now standard notation follows Landau
(Edwards 2001, p. 16).
It is an entire function (Edwards 2001, p. 16).
It is implemented in the