*Grin* I guess the question is, are there enough expressions of the complexity of this one, to make it plausible that every 106-significant-figure constant can be the value of one? Just eyeballing it, the complexity looks about right. I would echo Greg Huber's "Whoa!" if the expression were, say, half as long. I don't suppose Gosper is willing to show us N[%364,200]. Of course the *real* question is Veit's; just because a "representation" exists doesn't mean that it's easy to find, and I have no clue what tricks Gosper is employing. On Tue, Aug 4, 2020 at 1:28 PM Veit Elser <ve10@cornell.edu> wrote:
As someone late to the party, what trick is being use to create these conspiracy theories? My guess is that one tries to express the log of the target number (Gamma[1/4]) as an approximate rational combination of the logs of “the usual suspects” (e.g. golden mean), in the same way as subset-sum, where the approximation is set up as finding a short vector in a lattice using LLL.
-Veit
On Aug 4, 2020, at 12:39 PM, Bill Gosper <billgosper@gmail.com> wrote:
Out[364]= Gamma[1/4]==(1+√√5)^(3/2) √(5 (1+√2) (√2+√√5)) (1+√5)^(11/4) √√(3+√10) E^(-65π/3)π^(3/4) Sinh[20π]/2^(11/16)
In[372]:= N[%364,105]
Out[372]=3.62560990822190831193068515586767200299516768288006546743337799956991924353872912161836013672338430036147
==3.62560990822190831193068515586767200299516768288006546743337799956991924353872912161836013672338430036147
—rwg
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