5 Jun
2020
5 Jun
'20
10:16 a.m.
Simon Plouffe's old http://wayback.cecm.sfu.ca/cgi-bin/isc/lookup?number=1.64163256065515386629&... told me that In[202]:= Dot @@ Table[{{1/2 + 2^-n, -1/2}, {-1/2, 1/2}}, {n, ∞}] = {{1,-1},{1-𝜗, 𝜗-1}] (if only Mathematica supported infinite Tables) where 𝜗 = In[186]:= Sum[2^-Binomial[n, 2], {n, ∞]}] Out[186]= EllipticTheta[2, 0, 1/√2]/2^(7/8) I.e., this product converges to something interesting even though the determinant approaches zero. I can't wait to try other things, but agonizingly, Simon's website seems up only a few seconds every few minutes! —rwg