A249023 Decimal expansion of Tangent Euler constant.

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

Offset

0,1

Comments

The Tangent-Euler constant is introduced here as the limit as n increases without bound of sum{tan(1/k), k = 1..n} - integral{tan(1/x) over [1,n]}; this is analogous to the Euler constant, defined as the limit of sum{1/k, k = 1..n} - integral{1/x over [1,n]}.

Links

Table of n, a(n) for n=0..24.

Example

Tangent Euler constant = 0.9943228747334639280815980...

Mathematica

CI = N[Integrate[Normal[Series[Tan[x], {x, 0, 500}]] /. x -> 1/x, x] /. x -> 1, 100]; t = (Total[Table[((-1)^(n - 1) 2^(2 n) (2^(2 n) - 1) BernoulliB[2 n])/(2 n)! HarmonicNumber[k, 2 n - 1], {n, 80}]] /. k -> #) - N[Integrate[Normal[Series[Tan[x], {x, 0, 10}]] /. x -> 1/x, x] /. x -> #, 100] - CI) &[N[10^30, 30]]
RealDigits[t][[1]]
(* Peter J. C. Moses, Oct 20 2014 *)

Crossrefs

Cf. A001620 (Euler constant), A249022 (Sine Euler constant).

Sequence in context: A118739 A192031 A283749 * A336044 A019893 A346585

Adjacent sequences: A249020 A249021 A249022 * A249024 A249025 A249026

Keyword

nonn,easy,cons

Author

Clark Kimberling, Oct 22 2014

Status

approved