A346713 Decimal expansion of sqrt(log 2).

8, 3, 2, 5, 5, 4, 6, 1, 1, 1, 5, 7, 6, 9, 7, 7, 5, 6, 3, 5, 3, 1, 6, 4, 6, 4, 4, 8, 9, 5, 2, 0, 1, 0, 4, 7, 6, 3, 0, 5, 8, 8, 8, 5, 2, 2, 6, 4, 4, 4, 0, 7, 2, 9, 1, 6, 6, 8, 2, 9, 1, 1, 7, 2, 3, 4, 0, 7, 9, 4, 3, 5, 1, 9, 7, 3, 0, 4, 6, 3, 7, 1, 4, 8, 9, 9, 8, 0

Offset: 0

Author

Peter Luschny, Sep 01 2021

Keywords

• nonn
• cons

Comments

Represents a transcendental number.

Examples

			0.8325546111576977563531646448952010476305888522644407291668291172340794351973...
		

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.

Links

• Index entries for transcendental numbers

Crossrefs

Cf. A002162.

Programs

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)

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 *)

Formula

Equals Product_{k>=1} (2/(2^(1/2^k) + 1))^(1/2).

Equals sqrt(2*arccoth(3)) = sqrt(A002162).