A249022 Decimal expansion of Sine Euler constant.

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

Offset

0,1

Comments

The Sine Euler constant is introduced here as the limit as n increases without bound of sum{sin(1/k), k = 1..n} - integral{sin(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..26.

Example

Sine Euler constant = 0.466599306203729265221734220...

Mathematica

f = DifferenceRoot[Function[{\[FormalY], \[FormalN]}, {((2 \[FormalN] - z) (2 \[FormalN] - (z + 1))) \[FormalY][\[FormalN]] + \[FormalY][1 + \[FormalN]] == 0, \[FormalY][1] == -1}]];
(Total[Table[1/((-1)^(n + 1) (2 n - 1)!) HarmonicNumber[k, 2 n - 1], {n, 50}]] /. k -> #) - (CosIntegral[1] - CosIntegral[1/#] - Sin[1] + # Sin[1/#]) &[N[10^35, 40]]
RealDigits[t][[1]]
(* Peter J. C. Moses, Oct 20 2014 *)

Crossrefs

Cf. A001620 (Euler constant), A249023 (Tangent Euler constant).

Sequence in context: A155907 A081261 A251738 * A270541 A046262 A147862

Adjacent sequences: A249019 A249020 A249021 * A249023 A249024 A249025

Keyword

nonn,easy,cons

Author

Clark Kimberling, Oct 22 2014

Status

approved