OFFSET
0,1
LINKS
Jean-François Alcover, Involute of the exponential curve (left branch).
FORMULA
Equals Integral_{-infinity..0} (sqrt(1 + exp(2x))-1) dx.
Equals sqrt(2) - 1 + log(2) - log(1 + sqrt(2)).
Equals sqrt(2) - 1 - arcsinh(7/(4*(5 + 3*sqrt(2)))). - Jan Mangaldan, Nov 23 2020
Equals sqrt(2) - 1 - arcsinh((5 - 3*sqrt(2))/4). - Vaclav Kotesovec, Nov 27 2020
EXAMPLE
0.22598715591349733298631152068808233761701168147556791654406413883...
MATHEMATICA
RealDigits[Sqrt[2] - 1 + Log[2] - Log[1 + Sqrt[2]], 10, 100][[1]]
RealDigits[Sqrt[2] - 1 - ArcSinh[7/(4 (5 + 3 Sqrt[2]))], 10, 100][[1]] (* Jan Mangaldan, Nov 22 2020 *)
PROG
(PARI) sqrt(2) - 1 + log(2) - log(1 + sqrt(2)) \\ Michel Marcus, Nov 20 2016
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, Nov 20 2016
STATUS
approved