Prod[1-(n+1)^3, n=1,...,Inf]

Eric W. Weisstein eww at
Tue Apr 18 16:00:01 CEST 2006

On Mon, 17 Apr 2006, Dean Hickerson wrote:

> Zak Seidov wrote:
>> Prod[1-(n+1)^3,n=1,...,Inf]=
>> Cosh[(Sqrt[3]*Pi)/2]/(3*Pi)=
>> 0.809396597366290109578680478726.
> The exponent should be -3, not 3.  (And it could be simplified to
> prod[1-n^-3, n=2,...,inf].)
>> Is this cons known?

The product is very similar to eqn (23) and might very 
well have a similar formula for arbitrary power.  Any takers?


> Not to me.  But Mathematica is able to evaluate the infinite product in
> closed form in less than a second, so presumably it's not hard to prove.
> Mma also gives closed forms for the product with the exponent replaced
> by other negative integers, in terms of trig, hyperbolic trig, and gamma
> functions.

More information about the SeqFan mailing list