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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

%I

%S 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,

%T 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,

%U 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

%N Decimal expansion of the excess of the exponential curve arc length over the length of the x-axis from -infinity to zero.

%H Jean-Fran├žois Alcover, <a href="/A278386/a278386.pdf">Involute of the exponential curve</a> (left branch).

%F Integral_{-infinity..0} (sqrt(1 + exp(2x))-1) dx.

%F Equals sqrt(2) - 1 + log(2) - log(1 + sqrt(2)).

%e 0.22598715591349733298631152068808233761701168147556791654406413883...

%t RealDigits[Sqrt[2] - 1 + Log[2] - Log[1 + Sqrt[2]], 10, 100][[1]]

%o (PARI) sqrt(2) - 1 + log(2) - log(1 + sqrt(2)) \\ _Michel Marcus_, Nov 20 2016

%Y Cf. A222362 (a similar constant).

%K nonn,cons

%O 0,1

%A _Jean-Fran├žois Alcover_, Nov 20 2016

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Last modified October 17 22:48 EDT 2018. Contains 316297 sequences. (Running on oeis4.)