Mathematica Asked on December 26, 2021
I’m running 12.1.0.0 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.
This is an answer as I cannot comment yet.
Is anyone else able to replicate this issue?
Yes, I can confirm that Mathematica 12.1.0.0 on Linux and Mac gives the answer 0, same for the odd integers greater than 5.
In Mathematica 11.3.0.0 the code
Product[1 - 1/n^5, {n, 2, Infinity}] // InputForm
yields
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.
Answered by A.Z. on December 26, 2021
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