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A278386 Decimal expansion of the excess of the exponential curve arc length over the length of the x-axis from -infinity to zero. 2
2, 2, 5, 9, 8, 7, 1, 5, 5, 9, 1, 3, 4, 9, 7, 3, 3, 2, 9, 8, 6, 3, 1, 1, 5, 2, 0, 6, 8, 8, 0, 8, 2, 3, 3, 7, 6, 1, 7, 0, 1, 1, 6, 8, 1, 4, 7, 5, 5, 6, 7, 9, 1, 6, 5, 4, 4, 0, 6, 4, 1, 3, 8, 8, 3, 0, 7, 4, 8, 9, 1, 6, 2, 0, 9, 7, 7, 5, 6, 6, 6, 6, 2, 2, 5, 4, 3, 9, 6, 9, 4, 1, 3, 8, 0, 4, 2, 1, 7, 4 (list; constant; graph; refs; listen; history; text; internal format)
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
Cf. A222362 (a similar constant).
Sequence in context: A233073 A275266 A223387 * A262614 A184296 A131133
KEYWORD
nonn,cons
AUTHOR
STATUS
approved

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Last modified May 29 11:22 EDT 2024. Contains 372940 sequences. (Running on oeis4.)