29 Aug
2018
29 Aug
'18
1:01 p.m.
I suspect it’s true, not fraudulent. Try: p = 42; Simplify[D[ 2 t + 2 Sum[(Cosh[n t] (Cos[t] Sech[t])^n Sin[n t])/n, {n, p}], {t, p}] /. t -> Pi/2] -Veit
On Aug 29, 2018, at 1:14 PM, Bill Gosper <billgosper@gmail.com> wrote:
π == 2t + 2Sum[(Cosh[n*t]*(Cos[t]*Sech[t])^n*Sin[n*t])/n, {n,∞}], (1≤t<2 ?)
Is anybody playing with this? I find it incredible. Is it one of those Borwein or Zagier type high precision frauds? Bibasic telescopy? Am I missing something completely obvious? Inconclusive plotting suggests it holds in a region of the complex plane shaped like a football silhouette centered at t = π/2 + 0i of width > 1 and height < i. (DIY or stay tuned.) —rwg