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[arctica]

Hello,

I would like to convert the following Scilab code that I generated into Fortran 95, but not entirely sure of how to deal with it. Two issues, one how to deal with an equivalent to linspace and secondly the recursive function in zeta_3.

// Riemann Zeta Function (all domains)

// Re > 1
function s=zeta_1(z,n)
n=linspace(1,n,n);
//s=0.0;
if z == 0
s = -0.5
elseif z == 1
s = %inf
else
s=sum(n.^-z);
end

endfunction

// Re < 0
function zfn = zeta_2(s,n)
// Riemann's functional equation
// Analytic contiuation for negative values
zfn = 2.^s .* %pi.^(s - 1) .* sin(%pi.*s./2) .* gamma(1 - s) .* zeta_1((1 - s),n)
endfunction

// 0 < Re < 1
function zs1 = zeta_3(s,n)
// Vectorised version
zs1=0
k=linspace(1,n,n);
zs1 = sum((-1).^(k+ 1)./(k.^s ));
zs1 = 1./(1 - 2.^( 1-s )).*zs1;
endfunction

Any suggestions would be most helpful.
Thanks

Lester

[mecej4]

There are no zeta functions here, if n is finite.

Try this for your zeta_1:

[arctica]

Thanks for the solution, I have coded and tested the three functions and all looks fine:

[arctica]

Given the function Zeta_3

[mecej4]

It is not clear to me what you want. If t is a real array, s = 0.5 + i.t is a complex array, not a complex number.

Will the following do, perhaps?

[arctica]

That worked fine, many thanks for the guidance.

Had to stick the write statement in a do-loop to get the columns right:

do i = 1, k
write(25,'(f15.12,1x,f15.12)') real_part(i), imaginary_part(i) ! write data to file
end do

[mecej4]

You could replace the explicit DO loop