25 Feb
2013
25 Feb
'13
11:19 a.m.
On Sun, Feb 24, 2013 at 11:21 PM, Bill Gosper <billgosper@gmail.com> wrote:
These bilateral products invariant in the unit disk may be common: Product[1 + (-1/2 + (I*Sqrt[7])/2)*z^2^n + z^(3*2^n) + (-1/2 - (I*Sqrt[7])/2)*z^2^(1 + n), {n, -oo,oo}] == I/Sqrt[7]
Product[((I + z^2^k)*(-I + z^2^(1 + k)))/(1 + z^2^k), {k, -oo, oo}] == -((-1)^(3/4)/(2*Sqrt[2])), Product[1 + z^2^k*(-1 + z^2^k)*((-1)^(1/3) + z^2^k),{k, -oo, oo}] == -(-1)^(2/3)/3 |z|<1. ==rwg
[...]
Multiplying the identities gives the curious, bilateral product Out[331]=Product[1 - x^2^k + x^2^(1 + k), {k, -Infinity, Infinity}] == 1/3 when |x|<1.
--rwg