[Scilab-users] Reimann Zeta function

[Heinz Nabielek]

Riemann !!! Do not mutilate names....

> On 29.11.2021, at 18:23, Lester Anderson <arctica1963 at gmail.com> wrote:
> 
> Hi all,
> 
> Found a bit of Matlab/Octave code to solve the Reimann Zeta function for values >= 0, not perfect but it's a start. Need to figure out how to deal with negative values.
> 
> Lester
> 
> // Reimann Zeta function:  valid for t >= 0
> 
> 
> 
> function f=F(x)
> 
>     
> f = 1./(gamma(t(j))).*x.^(t(j)-1)./(exp(x)-1);
> endfunction
> 
> 
> 
> function [z]=zeta(t)
> 
>     
> global x
> 
>   
> z = zeros(size(t));
> 
>   
> for j = 1:prod(size(t))
> 
>     
> if(real(t(j)) >= 0)
> 
>       
> if(imag(t(j)) == 0 && real(t(j)) > 1)
> 
>         
> z(j) = intg(0,200,F)
> 
>       
> elseif(t(j) == 0)
> 
>         
> z(j) = -0.5;
> 
>       
> elseif(t(j) == 1)
> 
>         
> z(j) = %inf;
> 
>       
> else
> 
>         
> for k = 1:1:100
> 
>           
> z(j) = (-1).^(k-1)./(k.^t(j));
> 
>         
> end
> 
>         
> z(j) = 1./(1-2.^(1-t(j))).*z(j);
> 
>       
> end
> 
>     
> else
> 
>       
> z(j) = 2.^t(j).*%pi.^(t(j)-1).*sin(%pi.*t(j)./2).*gamma(1-t(j)).*zeta(1-t(j));
> 
>   
> end
> end
> 
> 
> 
> endfunction
> 
> 
> On Mon, 29 Nov 2021 at 08:51, Heinz Nabielek <heinznabielek at me.com> wrote:
> Riemann zeta function !
> 
> Georg Friedrich Bernhard Riemann (17 September 1826 – 20 July 1866) was a German mathematician who made contributions to analysis, number theory, and differential geometry.
> 
> Heinz
> 
> 
> 
> > On 29.11.2021, at 09:39, Lester Anderson <arctica1963 at gmail.com> wrote:
> > 
> > Hello all,
> > 
> > I am interested in the Reimann Zeta function, but it does not appear as an option directly with Scilab (v6.1.1).
> > 
> > Has anyone already prepared a function for this?
> > 
> > Lester
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