I managed to sort the problem by reordering the functions and it now seems to work. If anyone can see a more efficient method I would be most interested.
Added the option to check for a complex input and values in the critical strip.
Works as a reasonable approximation, but not as numerically precise.
function zz=zeta(s, n)
if isreal(s)==%F
zz = zeta_3(s,n)
elseif s>0 & s<1
zz = zeta_3(s,n)
elseif s==0
zz=-0.5
elseif s==1
zz=%inf
elseif s < 0
zz = zeta_2(s,n)
else s > 1
zz = zeta_1(s,n)
end
endfunction
Lester
On Mon, 17 Jul 2023 at 11:41, Lester Anderson
<arctica1...@gmail.com<mailto:arctica1...@gmail.com>> wrote:
Hello,
I have made a function to approximate the Riemann Zeta Function (see attached),
but complex input only works by directly calling zeta_3(s,n).
Calling zeta((0.5 + 3*%i),1e6) gives an error message: "Complex comparison not
supported. Please define %s_2_s_custom() or check your code."
For example: zeta_3((0.5 + 3*%i),1e6) gives the correct result
0.5328149 - 0.0791223i
Any pointers on how to tweak the zeta(s,n) function to accept complex input.
Thanks
Lester
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