Re: [math-fun] about a certain François Mendzina Essomba and surprising pi formulas

Hello, I programmed the first one, is is not like the AGM, the number of valid digits is proportional to n, something like approx. (5/2)^n, here is the maple routine : # F.M. Essomba formula es:=proc(n) option remember; if n = 0 then 1/2 elif n = 1 then sqrt(3.0)/2 else sqrt(2.0*es(n-1) + 2)/2.0 end if: end; a:=proc(n) 3*2.0^n/315*sqrt(1.0-es(n)^2)*(256 + 597*es(n) - 1024*es(n)^2 + 542*es(n)^3-56*es(n)^5);end; a(10000) differs from Pi at the 3979'th position. a (4000) differs from Pi at the 1591'th position, confirming that it converges rather slowly. It is not a record calculation, but certainly original (IMHO). I have not tried the other ones yet. Have a nice day and bonne journée.