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Probabilities.RiemannZeta Function

Riemann Zeta function.

Pascal
function RiemannZeta(const Z: TCplx; n: Integer = 64): TCplx; overload;
Parameters 
Description 
Defines complex value for which the Riemann zetao function is to be calculated. 
Defines used number of terms used in complex series approximation of Riemann zeta function. 

the Riemman zeta function.

The Riemann zeta-function is the function of a complex variable z initially defined by the following infinite series: 

for values of z with real part greater than one, and then analytically continued to all complex z <> 1. The zeta-function satisfies the following functional equation: 

valid for all complex numbers z. Zeta function is related to Dirichlet Lambda and Eta functions by: 

 

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