OFFSET
0,1
COMMENTS
Represents a transcendental number.
REFERENCES
Ludwig Seidel, Ueber eine Darstellung des Kreisbogens, des Logarithmus und des elliptischen Integrales erster Art durch unendliche Producte, Borchardt J., (1871), vol. 73, pp. 273-291.
FORMULA
Equals Product_{k>=1} (2/(2^(1/2^k) + 1))^(1/2).
Equals sqrt(2*arccoth(3)) = sqrt(A002162).
EXAMPLE
0.8325546111576977563531646448952010476305888522644407291668291172340794351973...
MAPLE
Digits := 120; sqrt(log(2)): evalf(%)*10^91:
ListTools:-Reverse(convert(floor(%), base, 10));
MATHEMATICA
RealDigits[Sqrt[Log[2]], 10, 100][[1]] (* Amiram Eldar, Sep 01 2021 *)
PROG
(Julia)
using Nemo
R = RealField(305); _1 = R(1); _2 = R(2); H = R(1/2)
p = prod((_2/(_2^(_1/_2^k) + 1))^H for k in 1:300)
println(p)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Peter Luschny, Sep 01 2021
STATUS
approved