I'm running on MacOS X x86 (64-bit). The expression

Product[1 - 1/n^5, {n, 2, Infinity}]

yields 0 as output, which is clearly false. Wolfram Alpha gives the correct result. In fact, it appears that

Product[1 - 1/n^k, {n, 2, Infinity}]

for any odd integer $k \ge 5$ returns 0. Replacement of Infinity with a large positive integer gives the expected result. Is anyone else able to replicate this issue? I have a strong suspicion that this is due to some problem with handling the choice of complex branch.

  • $\begingroup$ I get the same result as W|A gives with 12.1.1. I do not have 12.1.0 installed any longer, so I cannot test that version. $\endgroup$
    – Szabolcs
    Jun 24, 2020 at 8:35
  • $\begingroup$ You can try to convert the product into a sum of logarithms $\endgroup$
    – yarchik
    Jun 24, 2020 at 10:03
  • $\begingroup$ Duplication of mathematica.stackexchange.com/questions/220493/… $\endgroup$
    – user64494
    Jun 24, 2020 at 11:13
  • $\begingroup$ On 12.0 I obtain the same result as W|A, so this looks like a regression.I suggest that you report it to Wolfram Support. $\endgroup$
    – MarcoB
    Jun 24, 2020 at 14:39
  • 1
    $\begingroup$ In v12.1, NProduct gives correct numeric results. $\endgroup$
    – Bob Hanlon
    Jun 24, 2020 at 14:59

1 Answer 1


This is an answer as I cannot comment yet.

Is anyone else able to replicate this issue?

Yes, I can confirm that Mathematica on Linux and Mac gives the answer 0, same for the odd integers greater than 5.

In Mathematica the code

Product[1 - 1/n^5, {n, 2, Infinity}] // InputForm


1/(Gamma[2 + (-1)^(1/5)]*Gamma[2 - (-1)^(2/5)]*Gamma[2 + (-1)^(3/5)]*Gamma[2 - (-1)^(4/5)])

Odd integers bigger than 5 also seem to work.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.