The Euler infinite product series definition for Riemann's zeta function requires that Mathematica use all prime numbers in the product series. Can anyone help me with the code that will give a numeric value for all the zeta function (s)?

  • 3
    $\begingroup$ The Riemann Zeta function is implemented in Mathematica as Zeta. Does that meet your needs? $\endgroup$
    – bbgodfrey
    Commented Feb 4, 2016 at 3:20
  • 6
    $\begingroup$ Take a look at this answer. Compare e.g. Product[1/(1 - Prime[i]^-4), {i, Infinity}]//N and Product[1/(1 - Prime[i]^-4), {i, 7}] // N, i.e. only the first 7 primes give a very good approximation. More on this topic can be found here Double series over primes. $\endgroup$
    – Artes
    Commented Feb 4, 2016 at 7:26
  • $\begingroup$ Thanks for your comments. Due to the press of business I have not got around to a proper evaluation. Later. Just a note: The infinite sun series of the Riemann zeta provides a numeric answer. Nice. The infinite product, not so much without a workaround. Right? $\endgroup$
    – Don
    Commented Feb 6, 2016 at 15:42


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